The cable channel known in Canada as Silver Screen has a lot of old British comedies like this in their library. I usually catch them when I’m working late at night.
Let me take a crack at the other two, which I might have seen recently on Silver Screen. I don’t remember the titles, just the basic plots:
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A small town is scandalized by a racy book they assume was written by the local GP, but it’s completely fictitious.
-
A low-ranking American officer is mistaken for a bigwig and ends up in charge of a British NATO brigade.
Am I close at all? Do either of those sound familiar?
Sorry. Your descriptions sound vaguely familiar, but 1 and 2 have already been correctly guessed and 3 isn’t either of your suggestions (clue: it’s to do with cinema).
Sorry, I missed the answer to 2. No idea about 3. 
“Is it true you went 12-for-12 with last year’s Maxim cover models?”
“That is an excellent question. Yes and no: March and I had a scheduling conflict, but fortunately, the Christmas cover was twins.”
Chinatown
Iron Man!
Correct!
Yessir
Allow me to float one out there:
“Okay, I know these look like computers… Totally not.”
No one’s got this one yet. I’ll repeat the hint I gave above: it’s a film that’s been mentioned previously in this thread, several times.
The Core
Got it.
‘You want to find an outlaw you call an outlaw, you want to find a Dunkin’ Donuts you call a cop.’
Raising Arizona
Correct
“Watch out for Sodomite patrols!”
“Well tanks fer nuttin!”
HaHa, a line I quote often. Caddyshack, of course.
That was quick!
I love that line too and quote it often.