There's a couple issues with BURs that I think could be improved on.

1. Stale votes.

Currently, BURs are allowed to be edited at-will by the creator until it's approved or rejected. However, people can also vote on BURs, and they can be edited after such votes are made. An edited BUR also doesn't kick the thread up to the top*. This makes it possible for a BUR to be created, a user upvotes a BUR, then for the BUR to be edited in a way which the user would not want to upvote, which said user never sees. This doesn't have to be malicious, the BUR creator might not have thought the change was a problem, or there had been a discussion leading to a change that a user might not have seen. Either way, it leads to a BUR having votes by people who wouldn't have voted that way.

So I propose that when a BUR is edited, all existing votes on it are removed, ensuring users have the opportunity to re-review the BUR without their vote counting for something they never saw.

(*) Even if a thread was simply bumped when a BUR was edited, given that a thread can hold multiple BURs it may not be easy to find which was changed. Or the user who already voted may simply miss the bump, leaving their stale vote on. So I still think it would be a good idea to remove the vote regardless of it being bumped or not.

2. Too many BURs in a thread.

As evidenced by topic #29959, there doesn't seem to be a limit on the number of BURs in a thread, allowing BURs to flood out other BURs already in the thread, inhibiting discussions and making it difficult to properly vote on the different BURs. It may make sense to limit a thread to having something like 3 or 4 BURs max. Maybe this can already be covered by the rules against spamming and being disruptive, but the BURs themselves could still have been done in good faith not realizing it would be a problem to have so many together at once. Alternatively, maybe limit the number of active BURs in a thread, so as some get approved/rejected (and no longer need much discussion), more related ones can be added to the thread. Though especially without some kind of 'go to first unread post' functionality, finding new BURs down deep in existing threads can be difficult. I'm not sure what would be best.

I wholeheartedly agree with point 1.
Nuking the votes and bumping the thread up when changes get made to a BUR seem like a good idea to me as well.
Keeping a log of changes made to the BUR might also be worthwhile... but that might be asking a bit too much.

Number 2 would probably be covered by the "spam" rule.

I would also like to make it so you can't upvote your own BURs. The same goes for other requests, actually.