I have a late 2012 mac mini that I've been using headless since January, connecting to it via Screen Sharing from my 2010 MacBook Pro. It was OK, not great, but good enough. I mostly ssh'd to it from the MBP and really only used the browser on the mini for a few things that were really convenient to do from the browser on that machine.
I updated to 10.8.3 a few days ago, and since then when I Screen Share and open Firefox (19.0.2), the screen doesn't redraw properly, and I need to move the mouse across the screen to expose the content of the page. Open a new page, go through the same procedure. When I connect a monitor to the mini, though, and use Screen Sharing, it's fine. I tried it with Safari, and it seems OK.
I did notice a little bit of this behavior on the entire screen (not just with Firefox) before the 10.8.3. update, but it was mostly limited to the edges and it didn't really bother me - I chalked it up to network or memory issues since sometimes I'm maxing out my 16Gb and pushing the CPU doing stuff for work.
I'll add just for the whole story that I do have VirtualBox on the mini that had a couple of ubuntu VMs loaded. Using the VM over Screen Sharing has always been a problem - I was only rarely able to successfully type text (like the login) into the VM terminal window...but I needed to SSH to the VM anyway since I do the rest of my work on the MBP.
The other thing to mention is these apps for my company that I'm using are all written in Java, which was also recently updated, IIRC.
I've seen the post about making a dummy dongle for the graphics display, but it seems odd to me that it only occurs (so far) with Firefox. However, having the graphics display connected does solve the problem.
I could switch to Safari for the rare times I use a browser on this machine, but I'm a) worried that there's some problem that I should address before it's out of warranty, and b) wondering what changed with the 10.8.3 update to make this stop working.
Thanks in advance for any advice or tips.