All this is answered by checking state licensing guidelines. They just require some amount of years of accredited (ACGME/AOA, or rather now just ACGME) post-grad education before being licensed to practice, in addition to boards of course.
The barrier to entry, however, for those thinking of shirking their residency once they are licensed is insurance -- you apparently won't be able to get it, i.e. you're under-trained and are probably going to face a suit, and you have no way to settle it except for out of pocket.
^^^^^this does make me wonder about moonlighting though. Although maybe that is a different sort of insurance? I don't know. Someone more seasoned on that subject should respond.
Does location of where you do your residency have an effect on where you can practice within the U.S?
Can? No.
Will? Sometimes. Residency is often where connects are made that will make you offers.
With that said, you could just **** off to some other state 800mi away and still land something nice if you know how to look and the place isn't saturated.
For example, if someone does residency in Missouri, after finishing and becoming a specialist, can they one day pack their stuff and start a practice in another state without restriction?
Licenses are granted on a state-by-state basis. So....the question then becomes, does this "someone" have a license in the non-Missouri state? If so, great! If not, well, he/she needs to get one first before practicing.
Are they bound only to states that recognize their residency training, or is everyone recognized the same in terms of location which they can practice after completing residency?
The accrediting bodies for residency programs are recognized nation-wide. Where a doc can practice is determined by where he/she has a license.
TL;DR ACGME/AOA-accredited residency programs are recognized by all states. Where you can practice is determined by where you have a license. You apply for a license after your step/comlex III. K? Peace.