I try to get right the things that I can, but I know there are all sorts of details I could never hope to get right, because my resources are limited and some things one just can't know for sure (especially when writing about different time periods and such).
For that reason I stick to fantasy and even with that I include a disclaimer. I know I'll get things wrong, and if I can fix them I will, but sometimes I also take artistic license. I'd just hate if somebody saw one of my liberties and thought that it was a mistake committed out of ignorance or shoddy research! But sometimes it just can't be helped.
That being said, if I see something "wrong" in someone else's writing, it might bother me, if I feel it was done out of ignorance or laziness in "research" (for this reason movies like "The Scorpion King" just bug the snot out of me--there is just about NOTHING historically accurate in that thing, so why did they bother "basing" it on history?), but if I feel it's just a liberty taken by the writer I'll probably be more accepting. (Granted, such liberties are more acceptable in a genre like fantasy as opposed to historical fiction.) The catch is, most writers don't include disclaimers and one really can't tell if an incorrect detail is truly incorrect or just created that way by the writer.
I guess the short answer to both questions is, these things tend to niggle at me, but it varies depending on the situation, the genre, and the size of the "errors" committed.