There are several possible causes for remaining bugs. By and large, the most prevalent issue is backwards compatibility with games that were originally begun several versions ago. Unfortunately, this may introduce certain issues that simply cannot be retroactively fixed. There may be workarounds, but beginning a new game is the only way to 100% avoid them.
At other times, the use of mods that alter mechanics, allow fast travel from non-standard locations, or the use of console commands can create issues that bork a quest. Reloading to a prior save before the issue occurred is the only surefire fix for that. (I know this doesn't affect console users, just throwing it out there as a general source of problems.)
And lastly, there are likely a few actual issues still hiding in there, but these come in only two flavors. 1.) The cause can't be found. They're likely the result of some really obscure combination of things done over the course of the playthrough and virtually impossible to reproduce. 2.) The cause is known, but repairing it is impossible as the fix for one thing would knowingly damage several other things beyond repair.
What I can promise is that it is possible to complete the game. I've played through 4 times and have only restarted a few times during the early days. First step should always be a verify / repair of the game's files. Second step is to reload to a point before the quest appears in your journal and speed through it again -- I also recommend playing through the quest without using fast-travel at all. Final step would be skipping that quest...or restarting the game.
I know that's a crushing prospect for some, but it's the price that we pay for these gigantic engines with thousands of moving parts. I wish I had a definitive answer for quests not resolving / missing map icons / missing or inactive NPCs / etc., but it seems like the engine just gets stubborn and refuses to clean its room, sometimes.
