It seems that the plug-in is outdated and it's bugged or not compatible with your browser. Latest version of the plug-in works flawlessly with modern browsers. You can check for the update of your browser or update Skype. During the update, the plug-in will also update itself. If you still experience problems, you can disable the plug-in from the Extensions/Add-ons section of your browser.
If you have manually downloaded the plug-in, go ahead and uninstall it (make sure all your browsers are closed) then perform a new installation.