I have noticed that playback of HD content on the BBC iPlayer website is choppy/low frame rate in Flash Player 11.3.300.214 in both Internet Explorer and Google Chrome on Windows 7 64-bit and 32-bit. Version 18.104.22.168/22.214.171.124 and earlier work fine. I have been able to reproduce this bug on several machines.
I am posting this here as I cannot find a bug reporting section so I hope someone from Adobe reads these forums.
I've just found a similar bug on Bugbase (https://bugbase.adobe.com/index.cfm?event=bug&id=3160650) with a reply saying that it will be fixed in the next beta so we'll see if this applies to BBC iPlayer.