Continuity mistake: After Jim Carrey crashes the car on the bridge and, we see in the long shots that the lamp on the half-broken post above him is swinging from side to side. However each time we cut to a closeup of Carrey's face, it is lit very evenly - although the only source of light nearby is swinging wildly.
Factual error: In the very end, when Peter is returning to town, as the train rounds the bend you can see much newer style electrical transformers on the power poles. If you look close you can see a modern style street lamp also.
Factual error: The locomotive used to haul the train that takes Mr. Appleton back to Liberty after facing judgement is an Alco Century series - which weren't around in 1951. Nowadays, the locomotive type is actually semi-vintage, but it is obvious that this particular one has been patched up and modified over the years. It has intercoolers, ditch- lights above the pilot and a blank nose where the lower set of headlights used to be. In 1951, the locomotive would have been a steamer, or an early EMD F3 or Alco PA Diesel streamliner.
Continuity mistake: When Jim Carrey's car goes into the water, it lands upside down. Then he is underwater and gets his coat off. The car is completely submerged at this point. When he comes up for air, the car is only halfway submerged with one of the ends sticking up perpendicular to the surface of the water.
Factual error: If you look carefully you will see that all the cars have license plates with 7 characters on the plates. California did not introduce license plates with 7 characters until the early 1980's.