This has never happened to me directly but I did have an experience once at Paris's awful CDG T2 where I got to the airport really early (as I'd never been there before), got to the check in area for air france (I was a qantas codeshare customer at the time) only to be totally confused by all the signage and people queueing haphazardly everywhere so I asked a staff member, who directed me into the wrong queue which lost me ~25mins. It ended up OK in the end but I wasn't impressed.
But what would have happened if I was in the situation where I'm "on time" for my flight (eg. get there 30mins before check in closes for example) but there are giant queues for check in, which would put me at risk of missing the flight? Do people skip the queue or is there some official leeway? Or what if you check in and then miss the flight because you got stuck at security?
I don't fly often so these are probably stupid questions but this is one thing I've always been anxious about with flying.
Usually when check in is about to end for a particular flight, they have customer service reps walking around the queue and calling out for anybody still waiting to check in for that flight. They then jump you ahead to the front of the queue. So as long as you're there in the queue you should be ok.