Film's setting is a problem.

I think the point about why the book is set in WWII was more or less answered some time back (a few years back, by my reckoning). WWII is the war Heller was in, and it's the experience he was writing about.

As to whether it's an anti-war movie, it seems that depends more on how the person you're asking understands the phrase "anti-war movie" than on how he or she understands the movie. It's safe to say, I think, that it's not exactly a pro-war movie.

As to any relationship to Vietnam, I didn't really perceive it. The book, as already noted, was clearly not about Vietnam, as it was written earlier; though that doesn't mean that movie couldn't possibly have some Vietnam influence. The "MASH" book was also written before Vietnam (though not published until 1968), but that doesn't mean the movie has nothing to do with the subject. In this case, though, it seems that Nichols et al. were guided more by an intent not to make it about Vietnam than the opposite.

WWII was the good war. The noble war fought to defeat fascism. These "facts" have become accepted as part of the American narrative. For another perspective however, one might concentrate on the Crime Dramas that the Hollywood studios churned out after the war to fill the second half of a double feature. Many of these pictures have come to be known as Films Noir and as such are now considered classics. A pervasive theme of Film Noir is cynicism, where the good guy never wins if indeed there even is a good guy. Movies that are filled with characters of ambiguous morality. Films with more sexual tension and sexuality than those made today even though censorship was heavily imposed in the 40's and 50's. Pictures that seldom have a happy ending. Films Noir were very popular with an American public that had suffered through years of Depression and War. A war that had inflicted terrible physical and mental scars on the participants and an overall feeling of malaise amongst the general public even though the U.S. had emerged victorious. Harry Truman once said that the only thing new is the history we don't know. What the history we do know should teach us is that there is no such thing as a good war. "Catch 22" conveys that lesson in a wickedly funny and in an incredibly entertaining fashion.

You obviously have one view of WWII and hold it in some kind of sacred regard. Is it too hard for you to imagine one airman who wanted out at some point? Someone who probably volunteered and was given a position of great responsibility as a bombardier but who got pushed too far and let his fear and rationality take hold of him to want to get out.

As much as WWII was about democracy triumphing over fascism, there was a lot more going on there. There were deals made BETWEEN democratic and fascist countries to basically turn over half of Europe into fascism in order to bring peace. There were corporations which became international juggernauts because of the war. (Look into how Coca Cola was handed bottling plants all around the world by the US government in return for providing US troops with soda, or how P&G was given 10's of thousands of acres of virgin forest to start their paper business in return for operating gun powder packing plants.)

As others have pointed out, Joseph Heller was, himself, a WWII vet so his feelings are as valid as any other vet's on the matter. Not only that, but Martin Balsam, who played one of the more twisted characters in the film, served in the Army Air Corps during WWII. Buck Henry, the screenwriter and actor in the film, is the son of a Brigadier General in the US Air Force.

And the kicker - Mike Nicols, the director, was born in Nazi Germany and fled with his family in 1939, when he was 8 years old. I think he might have a valid perspective on WWII!