I encountered most every bug during launch, so put together this list of outstanding items and any helpful tips I have come across.

Pending Missions Award
Missions are getting stuck, cannot be redeemed, so filling up your quest log. This was supposed to be fixed a couple patches ago, if you are still encountering this, create an in-game bug report.


Disappearing party/guild/ops chat
This was supposed to be fixed a couple patches ago. Reload your UI and it should resolve itself. if you are still encountering this after reloading your UI, create an in-game bug report. Finally, try restarting your computer, as this can at least temporarily resolve the issue.

Graphical Issues
One thing i found is that my card was overheating. Playing in Windowed or Windowed-Fullscreen mode will severely heat up your Video Card (I was hitting 76C). Try playing in Fullscreen, and even disabling a second monitor. My temp dropped about 10-15 degrees with all high settings after this change.

A few user tips to modify windows settings to improve fps:
http://www.swtor.com/community/showthread.php?t=114264

"Must Complete Missions First"
Not an error, but stupid in game description if you as me. You will get this when your mission log is full and will need to either abandon or complete quests to add more!