Funny, I'm typing from Schiphol having just taken a flight there with KLM, and about to take another one with them. Everything seems fine, no large queues or long waits.
I know they'll probably help people out in this case, but who's generally responsible if there's an unusual wait and you miss your flight?
If you expect the usual 5 mins and there's suddenly 60, for example?
This might be kind of a snarky answer but it depends on what your status is with the airline. I have status with Delta and their answer always is “This was our fault let’s get you on the next flight”, at no cost, regardless of the situation.