1024 x 576 H.264 unwatchable due to video stuttering

The video is an mp4 and was encoded (by people who should know what they are doing) and is listed as being iPad friendly.

MP4 is a file container. Are we talking about MPEG-4 or H.264 (MPEG-4/AVC) video content in the MP4 container? (I.e., there are different display/data rate restrictions here for the iPad which may not apply to the video as being played back in iTunes. As to the audio, don't know why there would be a problem but knowing what the audio compression format/specs are might give us a starting point for possible problems.

You must convert them to m4v format with HandBrake, even HD 720p is playing smootly then 😉

http://www.handbrake.fr/

Video formats supported: H.264 video up to 720p, 30 frames per second, Main Profile level 3.1 with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats; MPEG-4 video, up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats; Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format

Make sure the file conforms to the above.

If you use HandBrake it will be the use the right formats!

you should convert it to HD(1280x720) for your ipad