Having seen this through much younger eyes a few decades ago, my faulty memory banks recall this as being: A) much funnier than I think it is now, and B) in glorious Technicolor, which it obviously wasn't.
All great comedians steal from each other, and many of the sight gags here owe so much to the great Ernie Kovacs, (who himself owed everyone from Buster Keaton to Harold Lloyd to old Warners cartoons and comedic shorts). That said, Jerry puts his own unique stamp on every gag, in that way which is what only the most gifted comics can pull off.
The recording studio sequence is much funnier than I remember it, and I would willingly sit through the first act just to get to it. There are a lot of dull spots, strange interludes that are compelling if somewhat jarring in the context of things, (his encounter with the 'live' puppets), and just a tad preachy, (the confrontation between T.P. Paramutual (Brian Donlevy) and his 'toadies' in the screening room.
Overall, I don't know if I would hail it as a masterpiece, (I will leave that task to Parisian critics,) but it's one helluva lot funnier than a lot of the crap coming out of Hollyweird these days.
I'd recommend it, but not over THE LADIES' MAN. Now THERE is a funny movie!