I have been doing fleet events and STF's today and the lag is just awful. While doing Starbase Blockade I actually thought my PC had froze for a while, but it just took 30 seconds for all the enemies to load. The "fight" consists of me watching my ship rubber-band back and forth across a mess of enemy ships as I frantically click buttons on my skill bar that take whole minutes to activate.
This is why STO is primarily a single-player MMO. Not because the players don't like doing group events, its because the servers can't handle more than 20 or 30 ships in the same instance.