The Thin Man was a great series of movies. I've looked for it many times but can never find it. I do remember that Myrna Loy and Asta did not get along. Asta even bit her once.
I found this: Yes, the dog Asta, played by Skippy, did bite Myrna Loy (who played Nora Charles in The Thin Man) once during filming. Loy mentioned in her autobiography that the bite occurred, and that their relationship was not particularly friendly as a result. However, the incident didn't stop Asta from becoming a popular character, and other dogs were used as substitutes after the first few films.