Continuity mistake: When Odie comes out on the porch to keep Garfield company, his collar and tags are visible; even more so when he attempts to get back in. But when the shot pulls away to show Odie alone on the steps (before running off after the scooter), his collar is gone. Part of the plot hinges on Jon trying to find Odie, who wasn't wearing his tags.
Continuity mistake: When Garfield rescues Odie and Happy Chapman picks up Odie he puts the shock collar on him. It then cuts to the dogs howling and then cuts back to Happy Chapman and you can see that the collar is no longer around Odie's neck but in Happy Chapman's hand. It then cuts back to the dogs and then back to Happy Chapman and the collar is back on Odie. He then starts to run and the collar is off again.
Continuity mistake: Garfield has a thumb on his front paws, giving him 5 digits on the bottom of his paws. He is shown leaning on a window and all 5 are making contact with the window as a human hand would. The paw print that Jon finds and recognizes as Garfield's are normal cat prints with only marks from 4 digits. If his paw did have 5 digits as seen in the window, he would have left a 5 toed print.
Revealing mistake: When Garfield and Jon first bring Odie home, you see Garfield talking to one of the neighborhood cats outside while Jon has gone inside with Odie. You can see a colored square on the sidewalk where the neighborhood cat sits. Throughout different shots in the scene you see the square disappear and reappear.