"The Cheap Detective," as others have observed, is a sendup of two of Bogart's most famous films. The film's opening sequence sets the stage of the humor styleings which acts as both a setup and warning for the casual viewer.
The humor is smart, but almost too clever for its own good. It's funny, but you almost have to be a Neil Simon fan (or at least in tune with his writing style) to really get the gags. Not entirely true, because if you keep an open mind, and understand all or most of the references, you should have a good time :-)
Otherwise the film might go over your head, or rather you'll understand that there's supposed to be a joke at a certain moment, but won't get the entire gist because you might be unfamiliar with the material being referenced. Hence the reason why I called the film almost too clever for its own good.
It helps to be familiar with both "Casablanca" and "The Maltese Falcon" to really get all of the "in-stuff" within Simon's film. Even so there's a good amount of regular humor that should help boost the appeal to those already in the know, and at the same time salvage a film for those not.
And yeah, Anne Margaret never looked better :-)
A fairly good watch, but not for everyone.
