Related to the question on the current flurry of novice users what is and what should be the period of time that a closed question can still appear on the site?
A closed question is just that: a question that was closed. Closed questions do not always represent bad (especially in the case of a duplicate). In some cases it's a good thing to have closed questions stick around.
With that being said, here's how the deletion process works:
48 hours after a question is closed it is eligible to be voted for deletion by anyone with the moderator tools privilege [1,000 rep in beta, and 10,000 rep afterwards]. Trusted users [2,000 rep in beta and 20,000 afterwards], on the other hand, can vote to delete immediately after a question is closed.
Once a post gets 3 votes to delete, it is deleted. However, note that even deleted questions can be visible by "moderator tool" users - which includes you!
Additionally, anyone can delete their own questions (I believe after 24 hours).
Also note: Moderators (people with the diamond) can delete a question at any time. If you really feel a question should be deleted, give one of them a call for help by flagging the question.
A closed question can be seen indefinitely. I doubt that that's going to change, although I suppose one of the Stack Exchange employees can speak with more certainty to that question.
It is also possible to delete a question, but being of poor quality is not usually enough of a reason. See the deletion section of the FAQ.