The native resolution for your L2610NW is 1920 x 1200 and the Mac Mini supports that using the HDMI port.
With the monitor connected, reset the PRAM as per > About NVRAM and PRAM
1. Shut down the computer.
2. Locate the following keys on the keyboard: Command, Option, P, and R. You will need to hold these keys down simultaneously in step 4.
3. Turn on the computer.
4. Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.
5. Hold the keys down until the computer restarts and you hear the startup sound for the second time.
6. Release the keys.iMac, Mac Mini, iPad, iPods, Mac OS X (10.6.8), (10.8.2), Safari, iTunes, iPhoto
Just received a new Mac Mini and in the same boat, using the same monitor. I tried resetting the PRAM (twice) and still get an "out of range" on my monitor. Verified the monitor works by connecting it to the HDMI out on my wife's laptop.
Any other suggestions?
Sorry, I have poor message board discipline. I eventually went and bought a mini-display port to VGA. The problem is the monitor from what I can tell. Going in analog (VGA) is the best way to avoid whatever digital handshake hangup these two are having. Best I can do.
My advice is call Applecare since you should still be under warranty and possibly schedule a visit to an Apple store where you can bring both the monitor and the Mac Mini in and demonstrate the problem. I agree with you 100% this should work out of the box with no issue, especiallty since your wife's laptop had no issue.