Can a Mac Mini have 3 external monitors connected to it?
Yes, a mac mini can have multiple monitors connected to it. There are now very good USB to Video solutions on the market that will correct this limitation.
Steps:
Choose a good Mac compatible USB to DVI or USB to VGA adapter. There are many available from different manufacturers. Look for adapters that contain the DisplayLink chip as these are Intel-Mac compatible.
Make sure you've downloaded the latest DisplayLink Mac Drivers, like these: http://sewelldirect.com/Drivers/DisplayLink-OSx-1.1.zip
- Install the drivers through the guided setup by first selecting the image file (.dmg) and opening it, accept the license agreement, select which drive to install the driver on (Macintosh HD), press the install button, and restart your computer.
- Plug your USB to Video adapter into your computer's USB port and attach your monitor's cable to the adapter. You can do this while your computer is on and it will recognize the device in the same way it recognizes most plug-n-play devices.
- Once your computer recognizes the adapter, it should automatically extend your desktop. If you prefer that it mirror the original monitor instead, or if you want to change any of the resolution settings, go to the Systems Preferences area and select "Displays".
When setting up multiple monitors choosing two of the same size is recommended.
Source.
I'd depending on your output resolution requirement I'd use a Triplehead2Go DP Edition to take a single output and split it into two (or three).
The obvious issue the th2g is that it not possible to to output higher than 4080 x 768 (3 x 1360 x 768). The device can do 5760 x 1080 (3 x 1920 x 1080) but the OS cannot choose the correct output settings.
You can also put dualhead2Go on the displayport output and then use the HDMI for the third monitor, this way each output on the dualHead can output up to 1920x1200 @ 50 or 60Hz.