At the outset I will say that my mini is so fault faultless, both with VGA on a range of monitors, and with DVI on my new 17" LCD, however, these are the issues that have been raised with it so far:
VGA display - dim, fuzzy or washed out. Many times caused by loose connections in the mini/DVI adaptor/VGA cable, sometimes by poor DVI adapters where the problem went away with a replacement and sometimes by poor calibraryion that can be corrected in the display preference pane. In some cases none of these fixes appear to work and some are suggesting the mini outputs below the standard level required for VGA.
DVI display - dark areas full of green or red 'static'. Some people have reported successful resolution by replacing the DVI cable, some people say this hasn't helped.
Displays general - reports exist of users who suffer from displays that go blank when the log in screen appears or when the screen goes from grey to blue, or at random when working. It seems that some monitors aren't being autodetected. These issues are normally fixed by manually entering display resolution and settings.
Hard drives - regular noise like a marble being dropped. This is something I have noticed on mine, though I also note the same noise (quieter) on a Sony Vaio and 2 IBM Thinkpads, so it's not mini-specific. Some claim this is a sign of failure, but my Vaio has made this noise since day 1 and it's done the equivalent of 100,000 miles with no sign of failure, so I doubt it's a 'failure' issue so much as an annoyance to some (I don't really notice mine unless I listen for it). Seagate make some of the drives used in minis (including mine) and seem to be indicating their belief this is normal (well, they would, wouldn't they) and that they are going to release a firmware update to reduce or eliminate the noise.
Noisy fan - the mini is typically very quiet, but some make noises that are described as likely caused by a fan with a fauly bearing. Not many complaints about this, but some.
Noisy combo or superdrive - it's normal for this drive to be rather loud when it spins up, but some report it stays nosiny once its running.
Again, I don't have any of these issues on my mini. I've tested it on a number of VGA CRT monitors and 3 separate analog LCD panels and had good and consistent results on each, and on a DVI LCD and had truly excellent display quality. My mini makes no annoying noises, runs quietly and behaves itself as perfectly as any system I've had. I'd have no hesitation in recommending it.