SuperDrive - one in five dvds won't mount
It would be good to know if the one in five is the same disk each time, or if it's more a case of roughly every 5 attempts the mount fails.  If it's the same discs everytime, then you could further troubleshoot by trying them in other devices.  If it's random discs, then it's likely your drive that needs troubleshooting.

Does it make any weird grinding noises, or excessive head seek operations before giving up on mounting?  And does it sometimes fail to eject the drive if it has failed to mount?  I ask because this is exactly what my iMac superdrive (2009 era) did.  Sometimes it would read, sometimes if would make awful noises, sometimes it wouldn't eject because it said there was no disc when there was.

I eventually removed it and replaced it with an SSD instead, and for the price of a few dollars on eBay I bought an external USB case for it to see if I could get it working at all - it's worked fine ever since!  Maybe just being rough with it and being able to shake it about and stuff when I removed it (in a way I couldn't so when it was internal to the iMac) helped?

If it is the drive, you have limited repair options other than percussive maintenance, a monster clean with a vacumm nozzle right down the slots, and re-seating the cables etc.  You could try putting your Mac Mini on it's side when inserting discs - sounds daft, but I've know this to work with failing drives.

As for replacing it, then any DVD drive is going to be absolutely fine if you just want to read discs.  Frankly you will struggle get a DVD-ROM, and anything you buy will be a writer also, but there is no need to go for the fancy options like dual layer burning, lightscribe lazer etching, Blu Ray playback etc etc.