Yeah I'm in the open beta. I'm really enjoying it - so far only a little bit of space is available (a small part of Federation space and Klingon space).
The missions are varied - you have "set" missions that you can accept, this will involve anything from investigating an unknown planet or abandoned space station, to fighting it out in space/on an away mission. There are also missions where you establish/maintain diplomatic relations. Some missions also form part of a story chain (with subsequent missions).
However, my favourites are the randomly-generated missions and fleet battles. An event will appear in space - be it a ship/starbase in distress or an enemy fleet movement. You can join fellow players in combat against dozens of ships, it's fantastic fun.

Another feature I really like is not only that you can play missions with friends in a "fleet" but if you go into a mission you join the "open instance" fleet and complete it with a load of strangers - or if you wish you can leave the fleet at any time and complete it alone.