If you are comfortable opening your browser's Developer Tools/Console, it will be helpful to look at the Network activity, specifically an XHR request going to wiki-ajax/?c=upload, and reviewing the response data from that request.
The browser's Javascript console may also reveal if there are Javascript errors.
I'm currently unable to reproduce the behavior described, so any new information will be helpful.
EDIT: I was able to reproduce the file dialog reopening on outer click when using Firefox.