Quicksilver pretty much nailed the UZR questions...
I would add that where the ball is hit makes a difference. A big one. One year there are a lot of hits to CC's diagonal left deep (deep LC field). He's got a pile of range in that direction. His UZR numbers spike from +10 to +18 in that year, the following year due to changes in the pitching staff and dumb luck few balls are hit that way and there are more flies/pops well within CC's range - bang down to a +5.
The only way to get a usable number is have a machine set up to sim all the different sorts of hits a fielder could get and grade them on that. That's a sim, that's not a baseball game or season or two.
For all of UZR's flaws it's better then other systems I am familiar with and well past things like FP% and GG's.