Mountain Lion Problems?

I recently upgraded to Mountain Lion. I've noticed that on some web sites featuring videos, instead of a preview picture showing up, there's a QuickTime icon with a question mark on it. Clicking on the icon, as you might guess, produces nothing, whereas before a video would launch

When I installed Mountain Lion I split the drive's partition into 2 parts and kept Lion on the other half of the drive because I'd read about how Mountain Lion had so many bugs, and I wanted the option to switch back if it was as bad as others were saying. If I boot the Lion partition up, everything looks good - the movie previews pictures are there, and if you click on them they launch. When I used my sister's MacBook with Snow Leopard, everything looked good and worked properly as well. This appears to be a Mountain Line "thing."

Before blaming the OS, Mountain Lion has many security features that I'm not familiar with. Is the video file on the site not being recognized because the OS isn't allowing access? Am I missing something? If I recall correctly, most of the videos were in mp4 format, which I would think is somewhat current.

Anyone have a clue what's going on here?

Thanks.