In a word: never.
But slightly more usefully, here's my 50øre. If you publish a paper that depends on the result, are you going to be embarrassed if the referee says, "Can you clarify your use of Theorem X?". If you feel happy saying, "A,B, and C all published result depending on it, so I figured I was safe." then go ahead. If you're not quite so sure that A, B, or C check things quite so carefully as you do, check it yourself.
So, for example, if it's a result about differential topology on loop spaces then I would check it very carefully because I ought to know about that stuff and I would be embarrassed if the referee said that. But, say, Kuiper's result on the contractibility of the general linear group, then I figure it's not quite my area of expertise and plenty of other people have used that result in the meantime that if someone finds a mistake now then my minor embarrassment is going to vanish into nothingness besides the other things that are going to come crashing down.
To put it a slightly different way, suppose that you prove X, which depends on Y. Then someone proves W depending on your X. Later, Y is found to be false. When you and the person who proved W happen to be at the same conference, do you a) hide in a corner and hope that they don't see you, or b) go to the pub and have a good laugh about it all. If you think it'll be (a), then you should have checked Y. If (b), then you're in the clear.