Have played from day 1 of head start, and here's a list of bugs I've found, most are persistent or very frequent:
High Priority:
Taris has major issues which are causing many people to crash, and keep crashing every time they try to use that character, effectively trapping that character forever. Many people including myself have decided to skip that planet entirely outside of class quests.
Medium Priority:
Mouse lock-up. About once every few hours, clicking seems to no longer work. My mouse shows up fine, but I can no longer use it to interact with the UI. Can be fixed by turning off and on UI. Starmap Lockup. This has happened to a few people I know a few times each. The planets on the map load up on glytched groups of symbols, and clicking on them zooms into a default planet with no travel option. Forces restart. (possibly only relog)
Low priority:
Follow doesn't work after about 10 seconds. Once I've been in combat a few times, my character glows green until I relog. Some heal's particle effect sticks. Happens to myself and all of those I group with, so it's either an Inquisitor issue, a Mako issue, or a general healing issue. Completing the objective for a daily quest doesn't always give credit. Speeder travel location tooltips stick on the screen if the map is closed while tooltip is active.
I'm not going to list all of the things that are just unnecessarily inconvenient or annoying that need hotfix changing, but all of these things really should be fixed pronto.