Anyone have a suggestion?
Don't use QuickTime - for anything. Seriously, just completely uninstall it from your system.
Instead, use VLC, KMPlayer or any other myriad media players which are infinitely better than QT.
Uninstalling is not the answer to me. I recently completed another project where the footage was shot on an Sony XD Cam and imported as 1440x1080. I exported the exact same way with h.264 – same settings and it plays perfect on QT. I cannot understand why this current project does not. These h.264 videos are being sent to clients and QT and Window Media is what they have to view them. If this doesn’t work, I have to send Flash which looks great through the Adobe Media Player.
I've had similar issues, and the way I've fixed it was to change the bit rate of the original comp in After Effects to 16 bpc. It somehow had gotten set to 8 bpc. You'll find the controller in the lower left hand corner of your AE file. Once I made that simple change, the flickering in the motion went away and my h.264 file played perfectly.