I have done the daily flashpoint every day except one I think since 1.3 and have done both the story mode ops each week, and so far, I have had only two bad experiences.
The worst was in a KP run. Only myself (tank) and one of the DPS had ever done it before. Several wipes from people not killing targets in the right order and breaking CC. When we got to the Fabricator, I was the only one who knew how to do the puzzle, and the other tank and both the healers were very undergeared and inexperienced, which means the other tank was not able to tank the boss the whole way. Eventually we were able to get through it, but it took about 2.5 hours for the whole run.
The other was in an EV run. We had an 11k HP healer who died and left after the first boss. We were able to 7 man the instance up through Soa, and had a wipe on Soa, then two DPS left. Finally after lots of waiting we refilled the group and were able to complete it.
Other than that, it hasn't been too bad. A few jerks here and there but nothing I can't handle.
I have yet to even try Operations out. But it's nice to know that there are at least some people willing to put the effort in if things go wrong. Starting to look like me and my friend are just unlucky when it comes to randoms, maybe we should look into joining a guild or something. Would fix the problem I guess. Kudos for finishing the operation though, my palm may have been permanently attached to my face if something like that happened to me.