Despite its more irritating aspects, this movie "works" in part because of a superb supporting cast of well-regarded character actors, all of whom are in excellent form. Charlie Ruggles' fluttery Major Applegate, Barry Fitzgerald's bibulous gardener, Walter Catlett's bumbling, self-important constable, May Robson's pompous dowager, and Fritz Feld's stiffly officious Dr. Lehman are as good a "bench team" as I've ever seen, and the fact that their distinctly drawn characters are so different from one another makes for much hilarity, especially in the jail scene near the end of the movie. The only real problem with the cast is that, as Hawks himself admitted later in life, everyone was a screwball of one sort or another (well, perhaps the two leopards and George the digging dog should be excepted), and therefore the audience lacked a character with whom to identify. Well, I didn't think Huxley was that much of a nut, and I definitely identified with his travails, for reasons that anyone who knows me will immediately recognize.
I watched the DVD of the movie twice, once with Peter Bogdanovich's commentary (complete with Bogo's imitation of Hawks' low, drawling voice). The commentary was lightly enjoyable but didn't really explain why this movie, which did not do well upon original release, has ascended so dramatically in terms of critical acclaim. It's funny how many films have been "reassessed" over time, but so little attention has been paid to "reassessments" of the original "reassessors." My verdict: Baby is fun to watch, but don't necessarily believe all the hype.