Continuity: When Dave turns into a dog on the highway, his robe shrinks to fit him instead of falling off as all his previous clothes had.
Factual errors: After the dog bites Tim Allen, it is taken away to the shelter to be tested for rabies. The standard test for rabies (and the only one that could return such rapid results) is the direct fluorescent antibody test, which is performed on a sample of the animal's brain tissue. Typically, the animal's brain or entire head is removed and sent to a lab for testing
Revealing mistakes: When Dave gets out of the shower, he stands in front of the mirror and shakes himself dry like a dog, but the mirror gets no water on it.
Continuity: As the 300-year-old dog escapes the lab, Dr. Kozak's hands shift places drastically between shots.
Factual errors: The music Josh Douglas sings is from the movie Grease, not the stage version of Grease. Also you can hear John Travolta singing Greased Lightening, again from the movie.
Continuity: Rebecca drops legal books on Dave's desk to get his attention. In the next shot the books are stacked again.
Miscellaneous: When Tim Allen is supposed to be naked in the lab you can see he apparently has underwear on under his lab coat when all the animals are escaping.
Miscellaneous: When Tim Allen falls over in his cage you can clearly see a pad in the cage that was not there before. This is probably a stunt pad to break his fall.
Plot holes: The dog shows up for the anniversary dinner with flowers. How did he get them? If he stole them, how did he get them wrapped?
Continuity: When the Judge asked for the counselors to approach her desk (in the courtroom,) her hand is shown off her microphone when the camera is not towards her, but when it is her hand is covering the microphone so no one can hear her. It happens so quickly that it is impossible for a human to actually do it in that much time.
Factual errors: When Dave is distracted driving to the courthouse, he slams on the brakes and the car slides to a stop. The age of car that he is driving would undoubtedly feature ABS (Anti-lock brakes) and therefore would unlikely slide in this manner.