I find STF Elites a lot of fun. They are small, quick and you have to coordinate to make them successful. This is the largest challenge in them. Unfortunately, it's also a major flaw. Most of the frustration I get from people, is that you don't need to run the Normal STFs before you take on the Elites. I've jumped into many groups where a PUG or two have no idea how to run it. I think we all want to jump into the Elites. Better gear, more challenging, but it causes frustration for the folks who have been in them more often than not.
There are a few things may help here.
1. Require that anyone who wants to run an Elite to run the Normal at least once.
2. Give a mission briefing when you queue. (i.e. ...Destroying one Cube in cure space may cause the Borg to attack the Kang. )
3. Give us a Vote to Kick option. It sucks, but I've been in a few where someone will come in, and just sit there or have no clue. I ran one last night (KA Ground) where the guy literally hung out until the rest of us completed the mission, then he walked into the room grabbed his loot and left.
4. If you get kicked, or the mission fails, allow you to re-queue immediately. It's very, very frustrating to be in a group only to have the Kang destroyed, then have to wait an hour to re-queue.
I think these will make running STFs more enjoyable for everyone.