I realize there have already been three or four threads on this but I think there are still some details that haven't been covered yet. (I'm trying to add a usage note and examples to the Wiktionary entry for 'sein', so I want to make sure I understand everything myself.) The rule of thumb seems to be that you use the Mir ist X construction when you're feeling X as some effect of the general environment, for example Mir ist kalt, Mir ist warm. But this doesn't work in all cases, as in Mir ist schwindelig, Mir ist langweilig, but Ich bin nass. Apparently it also depends on which of several otherwise synonymous adjectives you choose, for example Mir ist übel, vs. Ich fühle mich krank. Is there a list somewhere of adjectives that can be used this way? Perhaps there is a more accurate rule of thumb that works in more cases. Is there a list of examples, like Mir ist langweilig, vs. Ich bin langweilig, where the meaning changes depending on which form you use?
Constructions as "mir ist langweilig" are - though commonly used - actually incomplete because the subject is missing. Correct it would be: "mir ist es langweilig" or "es ist mir langweilig".
When you use "mir ist (es)" you're using a passive form and express a feeling you experience.
Es ist mir / mir ist (es) langweilig / heiss / kalt /
nass1 / übel / schlecht / schwind(e)lig / komisch.
1 This is out of the ordinary, and normally you won't say that. But: "mir ist es zu nass" is valid.
When you use "ich bin" it's an active form and you attribute a quality to yourself.
Ich bin langweilig / heiss / kalt / übel / schlecht /
schwind(e)lig2 / komisch.
2 This is out of the ordinary, and normally you won't say that.
When I posted this question I thought there would be a relatively simple answer, but it looks like the issue is more complex and far-reaching than I thought. There are similar cases which don't involve adjectives, e.g. Mir ist, als hätte ich ihn schon einmal irgendwo gesehen. (ref), and other cases which don't involve sein, e.g. Mir gefällt das Buch. (ref) I gather the technical jargon for the noun in this type of construction is 'Experiencer' (same in English and German). There is an article on this in German Wikipedia, though it doesn't go into a lot of detail; in English Wikipedia you get a redirect to a highly technical article on something called 'Theta role'. Googling '"Experiencer" German grammar' turns up a number of graduate level grammar texts and research papers which, although clearly relevant, were too technical for me to follow easily. The main takeaway for me was that in both English and German there has been a trend to replace dative 'experiencers' with nominative 'experiencers'. The result has been more incomplete in German than in English, and the upshot seems to be that the dative 'experiencer' construction in German is, while somewhat limited and idiomatic, much more varied than the (dative noun)+ist+(adjective from some list) I was thinking of. It seems that most basic texts on German choose to be vague on this and say something like "Certain adjectives take the dative case," without going into details, so I'd still like to find an exposition of this topic that isn't mired in jargon. But as far as finding a list of adjectives that take the dative, my thinking is now that even if such a list exists it would only account small part of the possible constructions that follow this pattern.