The misc quest to Visit the College of Winterhold has become permanently active in my quest log.

I persuaded my way past the entry person using the option that mentioned being the Dragonborn. It seemed like a perfectly legit thing to do, but the quest is still active in the misc quest log even though I've completed it.

I can only hope that this little problem will be rectified in a future update.

I know its only a trivial matter but I do hate loose ends in my Quest Logs.

Just out of interest, has anyone else had this happen?

yes, I have the same thing.