In my opinion, the evil / dark side-focused play of the Sith Warrior campaign is absolutely brilliant (playing it Light-sided is horrible). It could have been a movie on its own (heck, more than one). It's my personal main "head canon" playthrough of Old Republic, and I also used my Sith Warrior to complete the Knights of the Fallen Empire expansion. I'd say that the Imperial Agent campaign was pretty darn good too (very nice to see the Imperial Intelligence and how it operated; those guys were smart and efficient, and could have brought ultimate victory to the Sith Empire had it not been for the internal infighting between the Sith that essentially cripples the Empire, and often at the worst possible moments).
My three favorite campaigns were: 1) Sith Warrior, 2) Imperial Agent, 3) Jedi Consular.
As far as game-play related issues, the main one I have is the constant traveling through massive maps during the campaign. I know there's fast travel and eventually you get a short-enough cooldown on it, but you still need to get to point B to progress your story missions, and more often than not the amount of traveling necessary to finish x, y and z missions is driving me crazy (not to mention that the actual traveling speed via vehicles is negligibly better than just running, even at tier 3 vehicle speed which is supposed to be something like 110% running speed, but it really feels like 50%). And, obviously, the fact that the game more than shows its age, not just graphics-wise but also in terms of animations (they're very stiff and remind of me the kind of third person animation "quality" we had in games like Morrowind). And of course the fact that the combat is exclusively tab-target based (obviously an old engine like that wouldn't do dynamic combat).
I only play Old Republic for the campaigns though. I really don't play the actual MMORPG side of it. However, despite its shortcomings I am actually waiting for the next expansion, can't wait to see where that story goes, and can't wait to get in the shoes on my beloved Sith Warrior again.