There's a document on the Badminton World Federation web site called "Recommendations to Technical Officials" that says what umpires, line judges and so on can and can't do. The umpire can call a let for a line call if both the line judge and the umpire are unsighted (i.e. they couldn't see the shuttle land because someone was in the way). This is very rare--I've never seen it happen in a professional tournament. (I've seen it in local tournaments when there are no line judges.) If it's very close to the line, too close to be sure either way, then it's counted as in. The umpire shouldn't make a call in that situation.
Shuttles don't bounce, so the tennis-style "let - replay the point" can't happen. As has been said, the umpire will only overrule (immdiately) if an obvious error has been made; in either case, in or out, the rally was already over because the shuttle hit the floor.
In international BWF tournaments players may not be trusted on, and if a linejudge fails to see if it's in or out and the umpire hasn't seen it himself either he is allowed to call let. However, usually (depending on the level) players can also give their points away (i.e. they say well i saw it out so it's his turn to serve), this is also the case with national matches. If players cannot agree on the shuttle being in or out the umpire will call a let. Also in national matches it might be possible that an umpire onplay plays with only two (or sometimes even only one!) linejudges, in which case the linejudges take the opposite lines and the umpire checks the adjacent lines him/herself. In this case it might me very likely that the umpire wasn't able to see if it is either in or out, and if again the players don't come to a fast agreement he may give a let as wel...
