This highly depends on whether you are planning to use an existing game save or start a new game completely. Many bug fixes since the game released have been non-retroactive fixes (i.e. you have to start a new game for the "fix" to take effect). The DLC (add-on) bugs have not been touched and all of them are still there, because Bugthesda (I mean Bethesda) only patches the base game. Here is a list of all of the patches and issues that they have supposedly fixed: http://www.uesp.net/wiki/Skyrim:Patch
You can buy the alchemy lab for Breezehome if you have both Dawnguard and Hearthfire installed (Hearthfire seems to have fixed that issue which was caused by Dawnguard). As far as Pantea's Flute goes, I'm pretty sure that it still cannot be dropped (on an existing game), because that fix was non-retroactive (if I remember correctly). In the future if you see "unusual" items in a chest (like Pantea's flute, Rjorn's drum, Finn's lute, and certain "Rare Books") you may want to avoid taking them until you get the associated quest to find them. As far as quests to avoid, I could probably make a list "a mile long" of ones that have a potential to bug up, since things can easily go wrong in many situations during the game (see the paragraph below about saving your game often).
At this point, I would highly recommend that you start a new game so that the bug fixes that were non-retroactive will take effect in your game (should you run into them again). Another thing (which is very important) when playing the game is to make sure that you save your game often and backup old saves to an external area, if possible (e.g. Xbox 360 cloud, a USB flash drive, etc.). Also, don't rely on auto saves, in fact it is best to turn them all off, because they can eventually lead to save game corruption, freezing, slow loading screens and possibly other issues.