When Quaid shows the new guy where to safely hold parts on the robot they are assembling, in the next shot the new guy doesn't seem to take any notice and puts his hand in the unsafe position again and continues working.
In the first ten minutes when the characters are boarding the Fall, the female speaker says that they are now boarding the "7:15 flight." However in a conversation with his friend, they discuss having to wake up for their 6:00AM shifts.
The "London Underground" train, is actually of north American design despite bearing London Transport logos and the station showing London Underground posters. This is because the scene was filmed in a Canadian Subway station. The train also looks very dated, there are far more modern 'futuristic' trains currently in use on the London Underground.
For The Fall to travel the diameter of the Earth in 17 minutes, it would have to maintain an average speed of over 45000 kph (28000 mph). At this speed, it would be impossible for anyone to survive standing on the outside, because of both the airflow and the high temperatures resulting from friction.
If The Fall is free-falling and assuming no resistance, the occupants would be weightless for the entire trip. However people were shown in normal gravity except for the midpoint flip.
At 1-G the trip would take 42 minutes (a lot more than the 17 minutes as suggested in the movie), therefore the capsule has to be accelerating/decelerating at higher rates.
To travel 8,000 miles in 17 minutes the Fall has to have an average speed of 28,235 mph. At those speeds the ship would have to be traveling in a vacuum or the Fall would burn up with the friction of the air.
The music credits mention only Beethoven's Piano Sonata No. 17, but the first part Quaid played on the grand piano is actually from the first movement of Beethoven's Piano Sonata No. 14 "Moonlight" C# minor op. 27/2 - only the second piece is from the opening of the third movement of Ludwig van Beethoven's Piano Sonata No. 17 "Tempest" in D minor, Op. 31, No. 2.
When Quaid is being hooked up to the Rekall equipment, a technician starts an IV on his right arm. Despite the vein being clearly visible on his arm, she places the needle at least an inch to the left of it.
When Douglas/Hauser is lead to Matthias, they go underground to take what should be the now forgotten subway. The action is supposed to take place in the future in London but the subway station and car look definitely New-Yorkish and absolutely not like any of the London Tube.
When Doug grabs Lori in a chokehold during their fight, he points a revolver at her neck. If he had shot, he would have successfully blown his own elbow off, assuming her neck wouldn't have stopped the bullet. This type of grab/aiming at the neck happens again later in the movie.
At the beginning of the film, it's stated that "The Fall" is the only means of transport between the UFB and the Colony. So the 'invasion' would be simple to stop, but just destroying the tunnel used by the fall, i.e. blow it up.
When Carl leaves the rebel base in the wastelands he is wearing a respirator, but he enters the "helicoper" without passing through an air lock. Thus he would be exposed to what ever the respirator was meant to protect him against.
The Arabic characters written on the top left side of the passports are reversed , since Arabic is written from right to left , but when reading them from left to right they do make sense , they actually read "New Asia" which is the old name of the colony .
One hour into the movie Doug goes to check out a safety deposit box. After unlocking it, he carries it by the handle to a nearby table. Holding the box as so would cause all the contents of it would have fallen to one end. Yet when he lays it flat (horizontally) on the table & opens it, everything inside is neatly laid out & shows no signs of being tossed around.
When Harry and Doug are about to board the Fall, the announcement mentions that the travel time to the United Federation of Britain is 17 minutes. Seconds later, when the departure/arrival screen is shown on-board the Fall, departure time at the Colony is indicated as 01:35 and arrival time at UFB is indicated as 01:42, which makes for a travel time of only 7 minutes, and not 17 minutes.
During the zero gravity scene the empty cases ejected from Quaid's weapon are clearly blank rounds. Furthermore, according to Newton's 3rd law of motion, the shooter should have move backwards whilst firing.
The goof items below may give away important plot points.
In "The Fall" when Quaid flies in with a helicopter, he enters a room where he sets the explosives. Right before he enters that room, you can see from the window behind him that "The Fall" is moving. However, the release of it is shown after Quaid enters the room.
When Matthias is shot, you can clearly see black cloth on the robot's neck and shoulder areas where mechanical pipes and rods are supposed to be. They are visible in wide shots, however the black clothing can be seen on close-ups on the robots standing next to Melina.