When David begins to play Global Thermonuclear War, you hear the computer voice say the words as they appear on the computer screen, however, when it asks him to list primary targets, the screen also says "by city and/or county" yet the voice cuts out without saying that. This was likely considered unnecessary, as the words are visible on the screen.
When David is playing Galaga he is firing with his right hand. He stops firing to look at his watch with his right hand, but the sound effects being played are still the firing noises. David probably switched to using his left hand.
When playing Galaga the second time (when Jennifer asks David to change her grade) the audio of a Galaga sending down its tractor beam is heard, but that is not happening on the screen. The tractor beam could be in invisible mode.
When David and Jennifer are on the island trying to find a boat to leave the island, Dr. Falken comes in a helicopter. When they show the ground shots, it is pitch black out, but when they show the helicopter, the sun is either setting or rising in the distance. Most likely rising, as the scene take place just before sunrise.
When Mr. Lightman opens the front door to let Jennifer in, he has a pipe in his mouth. But in the very next shot when they're both inside, Mr. Lightman is holding the pipe in his left hand. He could have quickly removed the pipe from his mouth.
When David is asking about the list of games that he printed out earlier, he asks Jim why the list has games such as checkers and backgammon. However when David was printing the list of games, backgammon was not one of the listed games. David is adding Backgammon as an example.
As Joshua asks David to choose a country to play, you see a two (representing the Soviet Union) already typed in. When they do a close up of the screen, David is typing in the two that was already there. They were listed as options available to the player.
General Beringer orders his staff to 'scramble two F-16s out of Galena.' The aircraft later shown are F-15 Eagles. (This may be due to the script originally calling for F-15s, which were the front-line fighter in Alaska at the time.) Likely a slip of the tongue on the part of the General.
In the second scene, as the teacher is reviewing the test answers, he reads question number two and question number four. Question number two had just been answered but not confirmed, while Question number three had been omitted or glanced over entirely without any explanation. Question three could have been correctly answered by everybody, and thus not need reviewing.
Jennifer is already in the classroom before David arrives without her test while the rest of the class already has their test in front of them. This was obviously done deliberately by the director to show the audience she received an F.
Errors in geography
Just before the junior crewman "enables" the missiles a list of geographic coordinates (target locations?) appears on the video feed of the missile in the silo. The coordinates are all for locations in the Pacific Ocean. Since targeting data is preselected, this couldn't be the location of Soviet submarines. Possibly known patrol spots for Soviet subs – assuming it’s not a clue to the falseness of the test.
NORAD coincidentally using the same voice synthesizer as David Likely a standard make.
They Call the "43rd" Bomb Wing at Loring AFB near the end of the movie, But the 42 Bomb Wing was stationed at Loring. The 43rd was stationed in Guam. They could have recieved a temporary change in assignment.
As the WOPR is obtaining the launch codes, the missiles are shown to have the engines spinning up with the sound of a turbine engine. In the case of a Titan missile, this could be correct, because a Titan has two fuel components: Hydrazine and Nitrogen Tetroxide, which are pumped together by a turbine pump that is in fact powered by small amounts of these propellants. When the turbo-pump is on, it forces large amounts of the fuels together which spontaneously burn. When the pump stops, so does the engine.
When the relief crew arrives at the silo it appears they are in a snowstorm, as they are wearing heavy winter parkas. In the opening NORAD scene the guards are all in shirts - no jackets. This is unsurprising; US missiles are in many states. It's entirely possible, even likely, for North Dakota's weather to be different from NORAD's in Colorado.
When David is being arrested by the FBI, he is brought to NORAD. While NORAD is a military installation and not affiliated with the FBI, given that he is immediately brought to McKittrick and the others, clearly McKittrick asked to meet in person the teenager who'd hacked into NORAD.
In the 1980s it was not permitted for any Department of Defense computer with classified information on it to be connected to external communication equipment. It would therefore be impossible to dial in as shown. During one scene, the military technician exclaims that the phone company "screwed them", implying an external contractor allowed the connection against request and policy.
When David was asked why he had called back, he states that Joshua called him. They should be able to see via the trace that the call had indeed originated from Joshua. They probably want confirmation from David.
When David makes the reservation for Paris, he does so using Jennifer's name. Later, McKittrick asks who he is going to Paris with, but if he had found the reservation, he would have already known about Jennifer as well. Perhaps McKittrick assumes that Jennifer is a false name for someone else. 
At the start a captain and lieutenant take up duty at the Launch Control Facility. Shortly after taking up duty an audio "Go to war" signal is received. Part of the signal is Tango, Tango, Lima, Alpha (T,T,L,A) in writing it down to confirm correctness the lieutenant writes down T,T,A,A. If you look closely the lieutenant writes down correctly. The L is deformed but still readable as an L.
In the scene at NORAD when officials are trying to figure out what happened with the initial security breach, Paul says to McKittrick that the perpetrator broke in using a backdoor left in by the original programmer (i.e., Falken's password "Joshua"). That meeting also reveals that they took the backdoor out, but that the guy broke in again (note that David did not intentionally break in again - Joshua called David). The error comes when David is left alone in McKittrick's office in a later scene and proceeds to login using "Joshua." That password was gone by then (just as it is at the end when Falken tries to use it). They establish in the movie that the missiles would fire without a launch code if they thought NORAD was destroyed, which is what unplugging NORAD would convey.
At the beginning in the launch sequence, we see the officers enter the launch command sequence etc. into the computer. At the top of the display screen there is "WOPR Execution Order". The WOPR is the computer installed later to replace the missile launch personnel, and is a brand new device, so this screen display is a little too early. WOPR is the real name for Joshua who authorized the strike and existed at this point in the film.
There is a problem in this movie with time compression. They are racing against the clock to save the world, yet the two main actors manage to travel from Colorado to Oregon, play scenes with the scientist, and get back in what seems like a day or so. Corrected by JW PepperIt is approximately 2 days but that is well within a credible time frame for the film. When Joshua calls David the night David sees the TV news and calls Jennifer, the computer screen shows over 50 hours left in the game. The FBI grabs David the next morning based on that call from Joshua. The FBI immediately flies him from Seattle to NORAD (near Denver, CO); at most a 3-hour flight. David escapes NORAD a few hours later, hitchhikes and then flies to Oregon. The same afternoon he gets to Oregon and meets Jennifer, they find Falken within hours and spend no more than a few hours with him. Furthermore, just before Falken picks David and Jennifer up in his helicopter, we see a shot of the WOPR showing 9 hours left -- plenty of time to get back to NORAD around the time the game is ending, which is exactly what they do. Therefore, it not only is a plausible time frame, it is well executed by the filmmakers.
At the end after the "missiles" hit the air force bases and they find it was all a bluff, they cannot stand down the missiles because they are locked out of the WOPR. When the general tells McKittrick to "just unplug the damn thing", he says they cannot because the silos would interpret the shutdown as a destruction of NORAD and they would carry out their last commands which would be to launch. When they play Tic_tac_toe and tell Joshua to play himself, he hits the code to launch (not that this would work, since the code would not be found one digit at a time, either it's correct or not), then blows up a stack of circuits due to overload. Based on what Mckittrick said earlier, the silos would have launched the missiles. Corrected by Zwn Annwn It would make sense if all power to WOPR had been shut down due to the overload. However, since WOPR comes back and "talks" to them, it is obvious that it is still in control even with the blown circuits. Since it is still in control, it can countermand the order to launch.
Look at the launch code on the WOPR computer and make a note of it. Now look at the launch code at the end of the film - they don't match (someone set the cogs wrong on the WOPR). McKittrick says at an earlier point in the film that he can "change those codes in less than an hour" in case someone working with David has stolen the codes and plans to use them. We must assume that he has done this.
No wonder "Joshua" cannot launch the missiles - it's got the wrong code. Inside the WOPR, the code to launch the missiles reads "JPE 1704 TKS" - when the actual code which displays later on the big screen in the war room is "CPE 1704 TKS". McKittrick says at an earlier point in the film that he can "change those codes in less than an hour" so that anyone who may have stolen the codes can't use them. We must assume that he has done this.
As David and Jennifer sneak up the stairs to his room while his unaware dad is watching the news in the next room, listen carefully to the news anchor. The newsman says, "There has been an explosion in a prophylactic recycling plant." Obviously nobody recycles condoms, so this is probably an adlibbed joke by the fake news voice talent that stayed in the final cut. Corrected by Damian Torres Prophylactics are also rubber gloves, NOT exclusively condoms. There can be rubber glove recycling plants.
At the beginning, the missile silo launch officers are changing shifts. Both of the officers going off duty exit the control room before either of the two relieving officers enter, thus leaving the watch stations completely unmanned for ten seconds or more, not very likely for a strategic nuclear military facility. Though it's probably not officially a permissible procedure, it doesn´t mean there can't be a little "off-the-record" behaviour. These experienced men know fully well that they are the only ones down there as always.
Towards the end of the movie, when they are trying to get into NORAD, they crash their jeep into the fence and the jeep falls over. The next scene shows them running away from the jeep, and it's parked normally. The jeep that is parked normally is not the jeep they were driving. It was already parked on the inside of the fence before the crash. They crashed their jeep on the outside of the fence. As they run inside the gate and past the normal jeep, the crashed jeep can still be seen laying on its side on the outside of the fence.
In the scene where David is brought in by the F.B.I. for questioning, they mention he had reservations for two to Paris. However, when he put the reservation into Pan Am's system, it was done under the name "Mack, Jennifer K." Corrected by Grumpy ScotThey traced his recent calls after he hacked into W.O.P.R. and found the reservation. That's why McKittrick said "Who were you going to Paris with?" as they had nothing on Jennifer.
At the end of the film when Prof. Falken is typing responses to Joshua you hear Joshua's voice. Speakers weren't hooked into the computer. Where is the voice supposed to becoming from? The computer is hooked up to the building's PA system. Just because there are no speakers wired into the computer itself doesn't mean that it can't send sounds through the network connection.