Channel Hop: A production company example regarding the specials. The first two were produced by Lee Mendelson-Bill Melendez Productions, who also did the Peanuts specials, while the rest were done at Film Roman. In an interview with Bill Melendez, he stated that he had to drop the Garfield specials because Peanuts creator Charles M. Schulz didn't want his team to adapt both strips concurrently.
Deleted Scenes: The Comic Book Adaptations notably contained several scenes that are not shown in the actual specials. For example, in the adaptation of Garfield's Halloween Adventure, Garfield snatches a ring from the pirate ghosts' treasure chest. When he and Odie return home with their candy, they find the pirate ghosts waiting for them. After the ghosts chase them up a tree, Garfield figures out they want the ring back, so he gives it back to them and they disappear.
Missing Episode: Garfield's Judgement Day was a movie, then a special, that Jim Davis was forced to abandon due to being unable to find an animation studio willing to animate the film (possibly due to it being darker than the usual specials; the plot involved a tornado destroying much of the town). The story was released as an (currently out-of-print) story book.
As for ones that actually were made, Happy Birthday, Garfield, a hour-long documentary made for the tenth anniversary (which notably contained the only existing piece of footage for Garfield's Judgement Day and the very first Garfield animation from 1980, which adapted three very early strips and has the voice of Scott Beach), and Cartoon All-Stars to the Rescue, which has been legally forbidden to air again because Garfield was used without Davis' permission. (please note that Garfield showrunner Mark Evanier has officially debunked that last sentence; Davis did approve Garfield's use, but the agreement was always for a "limited" airing)
The Other Darrin: Sandy Kenyon voiced Jon in Here Comes Garfield. Thom Huge took over in the other specials (plus the TV series).
The December 1984 comic strip arc of Garfield re-meeting his family was recycled from the 1983 special Garfield on the Town.
Many, many one-off jokes were directly recycled from the comics, most prominently in Here Comes Garfield and the Christmas special. For example, the Christmas special took a punch line from a 1982 strip ("Why, just look at me. I talk to cats!").
Technology Marches On: Here Comes Garfield's third act relies on a distinctly 20th-century conceit: the idea that the City Pound will put down animals whose owners can't be identified or located, especially when they lack tags. Back when the show was made, the only real way to have identifying information on your pet was via collar tags, which many pets had difficulty wearing. For pretty much all of the 21st century, it's been common practice to have subdermal chips installed in your pets for ease of identification, so the whole incident would've been avoided (or Jon would've found out the Pound got called because Garfield & Odie were antagonizing the neighbors, which he remains blissfully unaware of).