When Rachel is dragged on the street by the dogs, she has no shih tzu with her, however in the very next scene, she explicitly says a shih tzu has bitten the guy the dogs went after.
Not long after Sam starts "Melt With You" at the shelter, you can see a lady handing Artie the same dog twice.
When Rachel, Sam and Mercedes are at the animal rescue and all the dogs start barking, there is a dog-trainer "barking along" with the dogs.