The scene where Garfield gets flattened against the back windshield of Liz's truck is a joke on the very popular Garfield plush toys that have suction cups on the paws, so they can be stuck on windows. Garfield even takes the same pose as the plush toy, with his front legs up diagonally.
Bill Murray has said during interviews that he hates that he didn't think to have Garfield say his famous Ghostbusters (1984) line "Dogs and cats living together... mass hysteria!" (in the scenes of Odie being introduced to the house) until after all post-production had been completed, and it was too late to add it.
In an interview, Bill Murray stated that he originally thought the script was written by Joel Coen. It wasn't until the recording process, and watching dailies, that he realized that it was written by Joel Cohen, not the same person, of whom he was thinking.
According to an article in Premiere Magazine, much of Bill Murray's recording sessions were done aboard the boat he was occupying while filming The Life Aquatic with Steve Zissou (2004) in Italy. Apparently, Murray wasn't impressed with the recordings he did while on land.
The animal trainer wore blue gloves and pushed the real dog off the chair. Then the blue hands were digitally erased. The CGI Garfield was animated, and matchmoved with the real dog. Then Garfield was composted into the live-action plate, pushing the dog off the chair.
This was the first film to air on The Hub, a U.S. children's television channel co-owned by Discovery Communications and toy company Hasbro (on October 10, 2010, at 12:00 p.m. EDT - two hours after launch).