Loading the dashboard for a 4.261 blog installation (ie, logging in as the administrator) shows a non-working Flash control, circled in the image linked below. In 4.1 there was a control panel which allowed me to dig into my website traffic. I've looked into the file mentioned there, but couldn't find a problem.
> http://download.oeko.net/bugs/mt4.20090701.1/mt-flash-applet.png
Reported on Movable Type 4.2
The flash files are stored in mt-static/flash so you might want to try reuploading mt-static.