#1) "The thing that might go wrong" = When we're doing something, we expect that some problem can happen (something might go wrong).
#2) "The thing that cannot possibly go wrong" = We BELIEVE/ THINK it is impossible for that kind of a problem to happen.
The difference is that we expect and prepare for some problems, like #1, and we can handle those. But we don't prepare for the problems like #2 (because we think they can't happen) and, as a result, it's impossible for us to solve them when they do happen.
Good advice! : )