Not too much to add here, as I agree with both of you. The best scenes are definitely towards the beginning. I especially love the moment where Stan looks into a mirror to confirm he is himself, after being confused by Ollie referring to him as Mr. Jones. The material afterwards isn’t bad; Stan has a couple funny lines and it’s always good to see Ollie’s reactions. However, the idea of trying to be quiet around a baby just is not a funny concept; it would of been much funnier if it was an adult like Walter Long they were trying to keep quiet around, as there would be a real threat to waking him up, sort of similar to the Merrie Melodies cartoon, A PEST IN THE HOUSE. Also, like Big Chief mentions, there are moments where you fear for the baby’s safety in some of these scenes (as opposed to PACK UP YOUR TROUBLES, where despite their ineptitude in taking care of themselves, they seem to be able to take care of Eddie’s daughter without putting her in harm’s way).
Now, the idea of Ollie taking on the motherly role is a decent idea, but not one that they take full advantage of after the initial scene of him getting Stan to stay. The lack of a musical score throughout beyond the credits also does not help matters.
It is interesting that this was the short immediately released after PACK UP YOUR TROUBLES, considering both deal with Stan and Ollie taking care of a child and both even feature director George Stevens in a small role. However, while PACK UP YOUR TROUBLES has the advantage of being a feature focused more on dramatic elements (which work for the most part, in my opinion), THEIR FIRST MISTAKE is a short film that simply tries to make comedy out of an idea that just doesn’t allow for much comedy. Overall, this one’s alright, but not super memorable beyond a few small moments.
7 out of 10