When Teri is trying to get Virgil to sign the word for "apple" his shirt alternates between tucked into his diaper and hanging out in different shots.
When Goofy is using the mop to knock the keys off the table, Virgil's collar is white. His collar is supposed to be blue at that point in the plot and is blue in previous and subsequent shots.
When Virgil is working with Teri in the University Dept. of Psychology he wants to play so he sets the hands of the clock to 4:20. The next time we see the clock it's set to 9:10.
When Dr. Carroll enters through a door at the top level of the vivarium to speak with Jimmy 41:51, he is seen carrying a flight simulator disk pack in his left hand. But a few seconds later at 41:54, he is seen walking down the staircase towards Jimmy without the disk pack in his hand. He is never shown putting it down anywhere.
The leather jacket Jimmy Garret wears is actually a Navy G-1 flight jacket worn by Navy aircrew. The Air Force did not begin issuing leather flying jackets to aircrew (theirs, being the A-2) until 1988, one year after the release of this film.
Jimmy Garrett's (Matthew Broderick) character is said to be a pilot in the movie, yet his rank is A1C (Airman 1st Class, E-3) which is a low enlisted rank. Pilots are Officers, 2nd Lieutenant and above.
As Virgil is taxiing the O-2 toward the runway the AP radios airport security that the aircraft is headed down taxiway 3. At all airports taxiways are lettered, not numbered. Numbers are used only for runways.
On Jimmy's green fatigue uniform, the Air Force Logistics Command shield is in the wrong position. He is wearing it on his upper right-hand side, when it should be on the lower right-hand side.
Jimmy Garrett (Matthew Broderick) is seen playing poker in an NCO club. Jimmy (and the rest of the table) is an A1C (E-3), and NCO (in 1987 when this was released) was Buck Sergeant (E-4, 3 stripes with a white center star) and up. The star in the center of the rank from 1976-1991 being not blue denoted an NCO. Airmen would not be allowed in an NCO club or an Officer's Club, there are Airmen Clubs for those ranks.
The name on Sgt. Krieger's locker is spelled 'Kreiger'.
When some of the chimpanzees are trying to escape from the bathroom window, it can clearly be seen that the screen has already been cut to allow them to get through it.
After the chimpanzees escape their cages in the vivarium, Dr. Carroll attempts to subdue Goliath with an electric prod stick, which Goliath grabs. As Dr. Carroll struggles to take the electric pod stick away from Goliath, Dr. Carroll falls on top of a desk 1:17:57 and accidentally kicks Goliath in the face with his left foot.
Jimmy is seen wearing an orange flight suit. Orange flight suits were phased out of USAF service by 1980.
The patch on Jimmy's fatigues is color. By 1983, the USAF had converted the patches on the olive drab fatigue uniforms to a subdued, more camouflaged version.
When they decide to take Virgil out of the complex, Garrett says "let's get the hell out of here" but his words don't match his mouth. His mouth movements actually say, "Let's get the f--- out of here."
When Virgil is with the animal dealer in Africa, South American macaws are visible in the background.
When Matthew Broderick's character Jimmy calls up Helen Hunt's character Teri McDonald late at night 57:08, he asks if she is Teresa McDonald. Teri does not correct him.