I cleared the requirements (killing the enemies) for the Forest Cleanup quest before picking it up from the quest board, and turned it in. Then I could still pick it up from the quest board, which leaves it in the available quests window, but naturally it's impossible to clear it (again).
The Pushy Protestants quest doesn't clear the first objective in the log, but you can still report it in the guild and complete it.
Also found some other bugs, but I think they've been reported. (Brainless Ring, various collision bugs)