Most of the bugs were due to not having enough server power for the amount of people. This caused serious amounts of lag and other issues.
A lot of people had problems killing "foulwing" the harpy queen. If everyone moved off the section of the mountain she was on (clearly and obviously defined space) then she would respawn. But what kept happening is that 100 people would all crowd in the spot waiting for her to respawn, which wasn't gonna happen. This was the case with most, if not all, open space boss mobs. If you were patient, you'd get to finish most of these quests.
Some of the other issues are things like materials occasionally spawning in places that you can't get to; ie nirnroots spawning on the face of waterfalls. This was fairly rare though.
Some searchable items would show up as containing items (it glowed) when in fact someone had already gotten the loot. Again, this was due to lag and was not a "bug" per se.
Another issue was that the beta was purposely limited to a level cap of 17. That meant that any quest that gets started earlier but requires level 18+ to continue just stopped. We were also limited to the first couple of areas for our races. So again, any quests that required you to go outside of those areas couldn't be finished.
My only complaint is the lack of bandwidth and server capacity for sustained gameplay. Hopefully this is fixed by launch.