Currently, there is a huge problem with blue dialog menus being used for griefing. These steal focus, making it impossible to do anything. The focus stealing is a seperate issue, but even if that is fixed, it doesn't prevent the problem.
Like with inventory offers, we need a mute button on permission requests, so that the offender can be quickly and easily muted. This is especially important in the (very common) cases where the owner has been banned, and you thusly cannot search their profile to mute them.
I've marked this issue as a bug, because this is a massive and gaping security flaw. It should not be considered a new feature to fix such an issue, that allows people to be crippled.
Aside from adding a "mute" button, possible fixes could be not allowing permission requests from a single object (or more than say, ten, by the same owner) to queue up at a time. Even with the option to mute the object's animation requests, hundreds or thousands could queue up by the time you hit the mute button on the dialog.
The ability to "close all" on these dialogs would be nice, as well. Possibly only closing all by the same owner/object or closing only permissions dialogs, so people won't be afraid of missing out on important dialogs such as money transfers, friendship requests, etc.