I fiddled around last night trying to connect the Mini 10v to an LCD TV using the VGA connection.
The first thing I learned the hard way - DO NOT enable (check off) the mirror display option in OS X System Preferences>Display.
You end up in a situation where all you get are vertical lines and funny windows both on the Min and on the external display and getting out of that mode is a real pain.
If you boot up on the Mini without the VGA cable plugged in, the mirror display option doesn't come up to uncheck it and if you boot up with the external display connected via VGA, you can't see the mirror display option to uncheck it.
In the second scenario, the box is actually there as far as the Mini and OS X are concerned and some people just kept clicking in the vicinity where they thought the check box was and eventually succeeded - I must have tried that for close to an hour and finally gave up and found a terminal command to turn mirroring off.
So as I said - don't ever turn mirroring on (unless you downloaded and installed a patch I saw on the net) or you'll have the same headache I did.
OK - to hook up VGA.
For one thing - the obvious way of connecting the external monitor or TV to the VGA port on the Mini and booting up the Mini does not work.
It should in my opinion, but all you get is a somewhat smaller display on the Mini - looks like a standard 3:4 ratio and nothing on the external display. My external display btw was a wide screen 32-inch LCD TV with a VGA input.
The way I got mine working is to boot up the Mini on OS X with nothing connected to the VGA output of the Mini.
Once the Mini was fully booted, plug the VGA cable from the external display into the VGA port of the Mini.
The display on the Mini should now change to just the background you had selected and it will go to the smaller screen and the Desktop of the Mini will appear on the external LCD display.
If it doesn't, go into System Preferences>Display>Appearance and drag the narrow white band on the top of the left display (representing the task bar) to the display on the right (which is your external)
Resolution will be whatever your external display is - you don't have to adjust anything. You can check that it's the maximum which will give you the sharpest picture.
One abnormality I noticed was the dock. I keep my dock hidden on the left side of the screen. That didn't work with the external. The dock still shows up on the Mini or you can move the dock to the bottom of the screen, then it shows up on the external display.
Tried the same thing with a 17-inch LCD monitor (4:3 aspect ratio).
Same procedure - just booting up the Mini with the external display already connected would not work.
If you already booted up this way, you can just unplug the VGA cable on the Mini, either wait or hit the space bar or touchpad - eventually the normal display will come back and then you can plug the VGA cable back in and proceed as above.