Deliberate mistake: As the Soviet tank starts rolling, the tank commander obviously uses a hidden step to mount the tank. Soviet T-55/T-62 type tanks did not have steps for mounting by the wheels and axles; to mount a rolling tank using the moving wheels or spinning axles would result in the mounter being immediately crushed and killed.
Deliberate mistake: In the scene where the FBI agents are transporting Lester Cowans in a car and telling him all his friends have confessed, for about three seconds the scenery goes by backwards. For some reason, the shot is played in reverse.
Deliberate mistake: When Hillary and CC are looking at Victoria after she's born, the baby Hillary's holding looks like it's several months old, not a red and pinched-looking newborn.
Deliberate mistake: In the end scene at the TV set, Scrooge tosses a coin out the window, and the camera follows the coin as it falls in slow motion. The people in the control room also watch this on their monitors. Problem is, this is a live broadcast and filming/watching something live in slow motion is impossible.
Deliberate mistake: When Barry is on the phone with Kent for the 2nd time (right before Barry invites Kent to the station), we see Dan (Alec Baldwin) in the booth trying to get Barry to hang up on Kent. Dan holds up a sign that says "dump HIM." Problem is, we are looking at a reflection of the sign, so the sign was actually written backwards, as a mirror image.