This movie contains examples of the following tropes:
Throw It In: Chance running full throttle into a sapling and then keeping on running (specifically the part where Chance implies that Sassy is fat when rushing off for breakfast) was done completely by accident by the dog actor. They thought it was somewhat hilarious, so they kept it in. Similarly, Michael J. Fox and Sally Field adlibbed the lines right after Chance ran into the tree.
Similarly, Chance stumbling when running through a field was given a humorous line. "Whoa! Gopher hole!"
Homeward Bound II: Lost in San Francisco:
The Other Darrin: Following Don Ameche's passing (the first Homeward Bound was his second-last film role), Shadow was voiced in the sequel by RalphWaite.
Not to mention at least some (if not all) of the animals were recast. Less obvious, but Chance's spots were a different color.