The original sweater that Jack gives Underdog is knit with a stitched in "U". When Polly calls Underdog, we can see that his sweater is no longer knit, and the "U" has an orange outline and is not stitched to the sweater.
When Jack is speaking to his dad near the end of the movie, Underdog is listening from behind a wall. In the previous scene he was wearing his new collar, but when he is behind the wall the collar is missing. The next time we see him, the collar is back.
The dog that they use for barking at the mailman is obviously not the one that is used in (most) of the rest of the movie. If you look closely at the patterning around the face, you'll see that on the barking dog's left cheek, the brown mark doesn't touch the lip, whereas the "main" dog's brown mark does. Also the barking dog has a softer outline.