Currently, there are no permissions to protect queries in the Advanced Search dialogue box from being modified (accidentally or not) by other users. I find this happens quite often, and it seems that sometimes, queries get modified without actually saving them (not fully confirmed through testing - just a suspicion). Because the queries we use are often used by multiple people, a change to a query may affect other user's views without them realizing it. This is particularly true of the dashboard - if you are using a query for a dashboard chart, and someone changes that query, you may not realize that your dashboard chart is no longer accurate.
Part of the problem seems to be with the design of the Advanced Search box. It has always seemed strange to me that queries are selected through an "Edit Query" drop-down. If this was separated out into a "Select Query" drop-down, with a separate Edit Query button, these accidental changes would be much less likely to happen.
Permissions on queries would also be helpful here. I know that you can currently select "Shared", but that is not granular enough. Permissions selections in Tech Groups would be a start, but would still lack granularity. When sharing a query, the creator should be able to define permissions on that query (allow admins full access). This would allow a user to create a shared query, but have it protected from editing by other users.