As we were having a discussion on IRC about pretender/prophet HP's due to dominion, and as I don't see it listed in the bug shortlist:
According to the manual, "For each level of friendly dominion in a province a prophet and/or pretender gains ... +10% hp"
Actual mechanic: For the average positive dominion of this turn and the last (or the last two turns, for hp during a battle), the pretender/prophet gains +20% hp. (negative dominion is -10%, as per manual)
So if you had a pretender w/ 100 hp, and were in dom 10, and then moved to dom 4, and then attacked somewhere whatever the dom, your hp would be
100(1+.2*(10+4)/2)= 240 hp. Manual would lead you to think that you should have 140 hp (based on the previous turn's dominion, or whatever if the current battle location's dominion were to be used).
similarly, if your 100 hp pretender was in dom 5, then went to a dom -5 province, and then attacked somewhere, it would have, i believe, 125 hp.
Just to keep it consistent,

, Str and MR effects due to dominion are based on the current dominion of the province the battle is taking place in.
enemy dominion lowers hp by 10% per pt, as per manual.
also, of course, as is well known, right clicking on the hp yields totally incorrect numbers
edit: I like averaging the previous two turns as a mechanic, personally, but the +20%/dom seems excessive.