saddlesore - I agree on all that and dry fire is a useful tool as you said, however, some people do insist that dry fire alone is enough. I've heard a number of people online and in person (sorry, I'm not going to go dig up sources) recommend spending time on lots of dry fire instead of going to the range.
Never just alone, by itself. You need to already know how to shoot live fire.
I benefited greatly from intensive dry fire practice on a daily basis back about ten years ago.
My gun club ran a regular match they called the Dirty Harry Match. It was a timed, action style, shooting match, with various stations (stages?) you move to, one after the other, with different tests of your shooting skill (each station involving at least one speed reload), from the draw, using steel targets at various ranges. It was double action revolvers only, .38 Special minimum caliber.
I decided to try out the training routine found in Ed McGivern's classic
Fast and Fancy Revolver Shooting. For a couple of weeks before the match, I dry fired (using exactly the method he laid out) hundreds of strokes per day, concentrating on doing it just right, doing various exercises in the book, soon developing a blister, later becoming a thick callus on my trigger finger.
I was amazed at what a double action shot I became at the end of the two weeks, doing only those dry fire drills. I scored third place, using the bone stock Combat Masterpiece I trained with (many used race guns), despite having a couple of hang ups due to cheap reloads inertia-pulling the bullets out under recoil, jamming up the revolver. Had I used better quality ammo, I would have totally dominated. I practically couldn't miss at any range.
That level of skill, however, only stays with you if you keep up the intense practicing. Let it go, and also goes that high level of skill. However, every day doing fifty careful dry fires would keep your skill up fairly high. Of course you must already know how to shoot live fire, and do it from time to time.