D.A.R.Y.L. and the doctor switch drivers while running from the police. When the car spins around, through the rear window an adult is driving and a child is in the passenger seat (at around 1h 12 mins).
(at around 1h 14 mins) During the car chase, when D.A.R.Y.L. and Dr Stewart swap places in the car, D.A.R.Y.L. can barely see over the top of the steering wheel, but at the end of the chase, the wheel is about at the level of his chin.
(at around 1h 14 mins) During the police chase on the freeway, D.A.R.Y.L. and two police cars jump the medium barrier, but only D.A.R.Y.L.'s vehicle survives the impact. While his car is slightly damaged, it is operational so that it continues against traffic in the oncoming traffic side of the highway. The damage consists of some fender wrinkling, the front right headlight of D.A.R.Y.L.'s car is no longer lit, and one of his parking lights is also out. However, in the next scene when he drives his car down the on-ramp towards the camera, D.A.R.Y.L.'s car is pristine with all of his headlights and parking lights lit.
At the beginning of the film, the 4-door, blue Chevy Nova Dr. Mulligan is driving (00:44 to 01:07) turns into a 2-door, gray Oldsmobile Cutlass (01:23 to 01:31), and back into a Nova (01:31 to 02:33).
(at around 26 mins) When D.A.R.Y.L. gets cash out of the ATM, the baseball kids in the background get out of the car twice.
(at around 36 mins) When Joyce teaches D.A.R.Y.L. how to play the piano, D.A.R.Y.L. demonstrates his grasp of the piece's rhythm by saying, "Whole note, two half notes, and four quarters to a measure", a perfect description of 4/4 time. However, they play a piece in 6/8 time.
(at around 1h 27 mins) Just after the Mach meter in the cockpit passes Mach 2 (twice the speed of sound), the aircraft passes over a small town at very low altitude, probably less than a thousand feet. At that altitude and speed, the overpressure of the sonic boom path would shatter windows, and possibly do greater damage.
(at around 1h 30 mins) When D.A.R.Y.L. ejects from the SR-71, he floats down to the water while attached to his seat. Ejection seats automatically separate. The parachute is not designed to support the combined weight of the pilot and the seat during the descent, and landing with the seat could fatally injure the pilot.
(at around 1h 27 mins) D.A.R.Y.L. flies the SR-71 at top speed while at treetop level. This was impossible. The SR-71 would top out at just under supersonic speed while at low level. The SR-71 needed to be above 70,000 feet in order to reach Mach 3 or greater.
The Lockheed SR-71 Blackbird has no sealants for the fuel tanks. The friction generated by high speeds heats up the skin, making it expand significantly. Expansion gaps are needed to prevent the skin from buckling or breaking due to the stress, like the tar strips in concrete roadways that allow the slabs to expand without damage. Therefore, after several supersonic sprints to heat the skin enough to fill the gaps, the plane takes off on nearly empty tanks, and refuels five minutes into flight. Otherwise, it will run out of fuel.
When D.A.R.Y.L., Turtle, and Sherie Lee play Pole Position (1982), the game appears to run far too fast for a 1980s console. While this is technically true, D.A.R.Y.L. is likely manipulating the game console, which is alluded to several times during the rest of the movie; e.g. the ATM hack, playing two games simultaneously while watching four different television programs, etc. Also he lowers the volume of all the screens without using a remote control, again with his mind.
(at around 1h 21 mins) When Dr. Stewart dies, D.A.R.Y.L. bends down to kiss his forehead, and the Doctor blinks slightly.
During the car chase, D.A.R.Y.L. and the doctor are supposed to be somewhere in Northern Virginia, but they're clearly in Orlando, Florida. One shot includes a billboard for RonJon's Surf Shop (at around 1h 11 mins). Another shot shows an exit sign for Orange Blossom Trail (at around 1h 12 mins).
(at around 47 mins) When D.A.R.Y.L. is in the private jet, he goes to the cockpit to learn how to fly an airplane, where a compass shows the airplane traveling at bearing 120 (ESE). He points to an aviation chart to a point near Blackstone, Virginia, but he claims this is 28°39.6'N. This latitude is close to Orlando, FL. He was pointing closer to 37°N.
When Turtle crashes while he is playing Pole Position (1982) on his sister's computer, the score on screen reads 39,750. Turtle tells his sister that his score is 41,500. Then, she pulls up the highest game score which is 41,500.
(at around 1h 15 mins) During the police chase on the tollway, D.A.R.Y.L. is driving on the wrong side of the tollway, while the police are chasing alongside on the correct side of the highway. While D.A.R.Y.L. is driving into oncoming traffic, he decides to get off the tollway. On the police radio, one of the policemen is heard saying that he (D.A.R.Y.L.) is taking an off-ramp. Actually, since D.A.R.Y.L. is driving into oncoming traffic, he would be taking an on-ramp going the wrong way.