Garfield shown as a kitten crosses the street there is a place he passes by called Lorenzo's Music Store which is a nod to Garfield's original voice actor Lorenzo Music.
The code that Garfield uses to unlock his phone is "061978", the date of the first "Garfield" comic strip (June 19, 1978).
The number on the waste container where Garfield is left behind is the date of the very first Garfield comic strip, "06-19-78" (June 19, 1978).
The scene of Jon bathing Garfield is reminiscent of the September 5, 1978 strip, where Jon is also seen wearing a helmet and gloves while giving him a bath. Likewise, the follow-up comic has Jon dry up Garfield, which results in Garfield being all fluffed up, much like in the movie.
In the scene where Vic tells why he left Garfield, there is a shop in the background titled "Jim's Comic Books" This is a nod to Jim Davis, creator of Garfield.