I think OP is just trolling. He asked about "common problems" before he even "placed the order".
Not in one comment has he said that he has contacted Apple, taken the Mini to the Genius Bar, etc.
Post a picture showing this post on your screen with the Mini in the picture, or it didn't happen.
I recently got a iMac Pro for work. The first one was semi-DOA (dead screen, but otherwise apparently fine - you could get the audio setup), I called Apple Support. The first support person was a dud, the next one was great, and stayed on the case so that I talked to the same person on multiple calls.
The support guy recommended return rather than repair saying "I wouldn't want to have a brand new computer repaired". I returned it to B&H, who cross-shipped a replacement, which has had no problems. The repair would have taken time, and actually I was in a better position with it bought from B&H because they had stock and Apple did not (custom configuration, but choose one that B&H stocks.)
You at least need to put forth some effort to let Apple remedy the problem. Call support or make a Genius Bar appointment.
I have a late 2012 Mini i7. It's been a great little machine, and that particular model is a gem. It's been having some trouble with driving monitors lately, but I've been running it with the video over-clocked for years - Samsung ultra-wide plus a 1040p monitor. Actually, the author of the patch for that gave up starting with Mojave, so I'd been running the screen at 30Hz, which is still over-spec. So, sometimes now you have to reboot it when the screen wigs-out. It probably needs a good cleaning, I've been afraid to because I've depended on it for work. I'll clean it soon. It seems to have problems when it gets hot.
6 years of good service, I can't complain.
As well, a late 2008 Aluminum Macbook that is still kicking no problems. Never had a problem with it, save for a hard drive that eventually started to die. I replaced it with a hybrid drive. (I replace the Mini Fusion drive(s) with a flash drive to improve performance and extend it's useful life, as well.)
I've no experience with the new Mini. We considered it, but for not that much more we got one of the best, big, bright screen available, 64GB of RAM, 8 cores instead of 6, and a real workstation Xeon processor. It's more costly but a better value overall.