Apple has released EFI Firmware Update 1.7 for the Mac mini, which addresses the frustrating flickering external HDMI monitors bug. From the release notes:
About Mac mini EFI Firmware Update 1.7
This update addresses HDMI video flicker issues on Mac mini (Late 2012) computers and is recommended for all users.
The Mac mini EFI Firmware Update will update the EFI firmware on your computer.
Your computer's power cord must be connected and plugged into a working power source. When your Mac mini restarts, a gray screen will appear with a status bar to indicate the progress of the update. It will take several minutes for the update to complete. Do not disturb or shut off the power on your Mac mini during this update.
Mac mini EFI will be updated to 0106.03
The update weighs in at a tiny 4.53 MB and can be downloaded directly from Apple's support pages here or via Software Update in OS X.