The only thing I can think of is the hard drive but then again, I worked on a desktop PC for decades where the tower was flipped on the side and it was fine. These weren't top of the line desktops either (Compaq/HP/Dell). I want to say you will be fine.
Also, give some consideration to H Mount, which is a reputable company that offers a mount for the Mac Mini (and has for years). They have provided a mount suitable for the Mac Mini to be mounted on the wall, under a desk, etc etc. I am not pimping the product as much as I'm saying that if it weren't safe, I doubt they'd still be pushing a product that does that. Perhaps.
It's fine to run the mini on its side. I run two of my minis in the Newer Tech side stand. They also run cooler (a few degrees C) on their side.
There is no issue with running HDDs on their side. Many enclosures (seagate, owc, newer tech, LaCie) run HDDs on their side.
Thanks, I should have looked at the MacMiniColo photo before posting...
I just moved to a new house that's pretty big, where the router is on the opposite side of the building. WiFi reception has been pitiful and I've been on the verge of getting the new Airport Extreme with more antennas to get better reception.
Until it hit me - put the Mini on its side. It's made of metal, so the signal only comes in through the parts that are plastic - the Apple logo on top and the circular bottom base. Now the Apple logo directly faces the router.
It made all the difference. Transmit Rates went from 7 at worst to 80 - 145. Now I can watch Netflix again - and the unit looks even more futuristic!
I can't see that.
On closer inspection, I can see that nothing is holding the Minis on their shelves though.