Traditionally, the words 'Star Trek' and 'mysteries' aren't ones you often see placed next to each other. Having done 90% of its lore building in an era before fan-forums and easter-egg hunting, it was far more common for the show's various writers to wrap up narrative threads rather than leave them dangling.
Almost all mysteries that were on the show were wrapped up by the end of the episode, with only the odd season-ending cliffhanger there to keep us guessing. Best of Both Worlds, Redemption, Scorpion, Chain of Command; these were Star Trek's biggest points of intrigue, but only ever for a few months.
But looking back over the show, a few tantalising questions were left unanswered. Some because the story being told didn't require them to be, and others because they were simply too good not to revisit at a later stardate.