The car Claude sells to the Stooges is a 1912 Winton Six.
Production number: 4093.
The tire-changing dilemma mimics one from a Laurel and Hardy short, including the un-tired rim falling on a person's foot.
The bit about the agent wanting to hire their car rather than the Stooges is reminiscent of a plot point in Sunset Boulevard, which was released two years later.
Matt McHugh (Claude) is actor Frank McHugh's brother. They looked and sounded alike, and were born 4 years apart. Matt, 1894-1971; Frank, 1898-1981.