A bug is an error (in performance) or a flaw (in design) in a game which prevents it from working as intended. This includes things such as graphical glitches, incorrect processing of player input, or other features not working properly. ArenaNet sometimes includes bug fixes in their game updates.
In contrast, an anomaly describes a situation in which one element of the game behaves inconsistently with other, similar elements, but it is not clear which behavior (if either) was intended. For example, Empathy triggers on missed attack skills, but Vigorous Spirit does not; the skill descriptions do not clarify ArenaNet's original intent.