Some rights that are based on reputation seem arbitrary (e.g. you need 250+ rep to vote to reopen a closed question). How are rights based on certain rep levels determined? Can they be changed once they are set, and if so how?
The reputation values associated with privileges are set by Stack Exchange and have remained largely unchanged since Stack Overflow was launched.
The values are configurable on a site by site basis - private and public betas have lower thresholds for most privileges (and higher for a couple) than graduated sites. For a full comparison see:
Values would be changed if it was felt that users were abusing the power - in which case the threshold would be raised to limit the privilege - or not using enough - in which case the threshold would be lowered.
I don't think 250 is too high. If five more experienced users (read: with 3,000 reputation or more) voted to close a question, they're normally right. IF you edited your question and it doesn't accumulate the necessary reopen votes, you can always flag for moderator attention.
Some have been the way they are before there even was a Meta (so the sites' owners/administrator made the decision), but some have been discussed here.