We have a server that only runs MySQL. I'm trying to increase its performance to the maximum, and I was wondering whether changing the
nice setting in my.cnf would have any favorable effect. Anyone?
Since the server runs only MySQL (ignoring OS related things) in general I would say no - the kernel is already going to take care of that for you since other applications (let's say Postfix or Apache) are not fighting for CPU slices. If it's the only major application running and already taking 100% of all CPU cores you're not going to get much more priority that that.
You're going to get more performance on the server by focusing on concrete bottlenecks - disk I/O, slow queries and tuning the InnoDB/MyISAM buffer/cache settings to match your server's usage patterns. The single biggest OS-level performance gain you can get right now is to replace spinning metal hard disks with SSD drives for your mysql storage - media cost and chassis factors though put this out of reach for many folks at the moment.