I just tried this with whatever was in my clipboard (just a URL) in Chrome and had no issues. I did have some issues in IE and I know roughly why (how the pasting system works). I'll move this to bugs though I'm unsure if there's much we can do. If you simply tap ctrl+v instead of holding it down that should prevent the issue.
I'm going to call this a partial fix as I've worked around it as much as I think we can. We now temporarily disable pasting when the paste is still being processed and that seems to help. With really complicated pastes, it may still be possible to trigger this (depends on the browser).