Revealing mistake: When Phil drives the truck off the cliff, you can see right through the grill of the truck (meaning there is no radiator or engine), and the transmission is also missing, as you can see when the truck is falling upside down. Without an engine or transmission it would be hard to drive off a cliff.
Visible crew/equipment: After Phil drives the truck off the cliff, and it explodes in a burst of flames, there is a shot of Andie MacDowell and Chris Elliot staring in shock at the disaster. The two actors are bathed in an orange glow supposedly coming from the flaming wreckage. But in the lens of the TV camera Elliot is holding, there is a noticeable reflection of the lighting equipment used to create the glow effect on the actors. (01:04:15)
Continuity mistake: When Phil looks out the window on the first Groundhog Day, he sees the right-turning truck outside the window just as the radio people shout "Groundhog Day", but on the first repeat of the day, the same scene outside the window occurs only after this exclamation is made. It couldn't be altered by him because he had just woken up.
Continuity mistake: When Phil comes around the corner, just before meeting Ned, there are two women walking together in the background. The one in blue is holding a yellow sign upside down that says Phil (the groundhog, not the character). The first 3 days in a row they are together as they should be. On the fourth day and every day thereafter the woman in blue is by herself which does not follow the exact day sequences. (00:21:25 - 00:35:25)
Continuity mistake: When Bill Murray has stolen the Groundhog and is driving away with it in the red truck, the police car and the TV van chase it. There is a shot of the red truck going under a low bridge, and then a long shot of all 3 vehicles. There is no way the TV van could have gotten under that bridge with all the stuff on its roof, and yet in the very next shot it is seen continuing the chase.
Continuity mistake: When Phil first meets Ned, right as he asks 'Did you turn pro with that belly button thing' there's a close shot of Phil where a man with a yellow hat and red collar walks behind him. In the very next shot, we can see the same man approaching from further down the street, then passing behind Phil again. (00:10:40)
Factual error: Phil departs from the office right after the 5pm news. Punxsutawney is over 90 minutes' drive from Pittsburgh. The sunset in Punxsutawney in early February is about 5.30pm, so by the time they get there it should be completely dark. But it's bright daylight, without even a hint of twilight. (00:05:45)
Other mistake: On the second day, Phil did his same tasks at about the same time as the previous day, so everything lining up the same made sense. However, on day 3, he quickly rushes out of his hotel, avoiding interacting with most of the people he did before and gets to the street with the beggar much sooner than he did before. Yet Ned still is there crossing the street and sees him exactly the same as before. However with Phil having skipped so much he would have gotten there and passed that spot a good while before Ned would have gotten there, and they should not have had the exchange again on day 3. Same thing for when he arrives at the Groundhog Festival, with Rita greeting him like he's late. But he would have gotten there much sooner this time.
Other mistake: Focusing on the clock as it turns to 6:00, one clock has a visible gear in the middle of the numbers. At other times, no gear.
Continuity mistake: When Ned first calls out to Phil, the Gift Shoppe store behind him has a sign in the display window saying "OPEN SUNDAYS 12 to 4", and a white poster in the door window. The remaining three times Ned calls out to Phil with that background, the Open Sunday sign is gone, and the poster in the door has changed to a smaller red sign. Also, vehicle positions have changed slightly, and the black truck's tire sidewall on the left changes position between first and remaining scenes. (00:10:20 - 00:21:25)