Issues such as these needs a few bits of information:
- need further information such as your graphics card and whether you have activated any graphics drivers in the Additional Hardware Window.
To find out what your graphics card is copy and paste the following into a terminal:
lspci | grep VGA
Assuming that you are using Firefox, try adding the Flash-Aid addon
If you are using Chrome/Chromium can you reproduce the issue with Firefox + Flash-Aid?
Confirm whether this is a Compiz issue or not.
Logout of Unity and choose the Ubuntu (Classic) and confirm whether the issue still occurs.
What's the quality of the Flash Video you are attempting to watch. HD quality flash videos are rarely achieved unless you have the newer ATI/NVIDIA cards & with their proprietary drivers installed.
Some people have reported issues on upgrading - these graphics issues sometimes "resolve themselves" if a new user account is created and used.
Since you have confirmed that its an Intel and the its still an issue in "no effects" - then that leaves the flash-video quality. If you have an issue with standard 240/360 Flash Videos, then its more likely to be the intel driver. Suggest file a bug report on Launchpad.
Also double check Firefox + Flash-Aid, and whether a new account resolves.