What are the negative aspects (no pun intended) of a dense negative apart from longer than normal exposure times? Let's say I overexpose a shot that it contains so much information that the frame is quite dark on the negative strip. It doesn't seem to have any information missing, so are there any problems really?
Wrong overall contrast (too high, in case of overdevelopment) and / or compression of highlights (bad highlight separation) in case of overexposure. Lots of other bad things, too
I agree with the pronounced grain problem. I recently accidentally overexposed and made some very dense negatives while attempting to capture a scene of a bridge in very thick fog. Yes, the detail is still there, and being an extremely flat image to begin with, contrast was not a problem, but oh, the grain. Especially with the film and developer I was using I expected a liquid appearance to the fog...
In Bruce Barnbaum's The Art of Photography he talks about the 12 useful zones of information that a film can yield; and ways to manipulate prints accordingly. I expose about 1-2 stops longer than meter reading in order to ensure detail in shadow areas. If the SBR is greater than 5, I don't try reduced development; but rather use some of Barnbaum's techniques for printing higher contrast negatives.
In addition to the above mentioned problems, you might have to buy some Potassium Ferricyanide to bleach the overexposed negatives so printing times can be measured by a clock instead of a calendar. Like doughowk says, overexposing can be used as a creative tool.