So two issues raised here: soldiers trying to find a general they like serving under, and secondly trying to find a better posting.

As for the first: Roman generals (legati Augusti) cycled through at a relatively brisk clip: the average term was 2-3 years (Agricola's seven years in Britain is the longest provincial tenure attested, and was exceptional). So if you hate your general and think he's an idiot, you basically can grit your teeth and wait him out.

We definitely know that Roman soldiers tried to switch units, although usually the motive is professional opportunity, particularly since there was an overall status hierarchy in the army from the fleet (lowest), to the auxiliary cohorts and then the legions (highest). For example, papyrus letters from a soldier named Claudius Terentianus show his enlistment in a fleet after his failure to get a position in the legions, his hopes of transferring to an auxiliary cohort, and his eventual transfer into a legion.

We know from centurions' careers that they routinely transferred from legions (as well as commanding auxiliary cohorts praepositus), and clearly these were positions that they sought out, through various personal and professional connections and a great deal of patronage. There is little evidence to suggest that Roman soldiers tried to transfer for other reasons (e.g. don't like the weather), although there is evidence of units proving reluctant to deploying to new locations (especially given that Roman soldiers tended to put down roots).

In short, probably very few transfers on account of the weather or bad leadership, but you might successfully transfer to a more desirable unit, or in pursuit of promotion and advancement.