I believe that is the debug version of Flash Player you're referring to. I get it myself on sites that have runtime errors.
If you're the developer of said site, then the best way to get rid of the "pop-up" is to get rid of the runtime errors. After all, it's there to help. If you are the end-user, then you should uninstall the debug version of Flash Player and install the general population version located at the Adobe website.
BTW - If you are the developer, then folks that run the debugger (like me, for instance) will see the errors pop up. There's no way for you as the developer to "disable" the debugger running on remote machines.
Here's a bit more info on the subject -http://tinyurl.com/35zpp5
If you want more detailed help (and you are the developer), I'd suggest posting the actual error messages that you're getting.