What software do you use when capturing video? Have you tried anything besides Blackmagic Capture Software (Blackmagic Media Express) like freeware VitualDub or commercial Premiere Pro? Do you get the same results using them?

What video codec do you use when capturing? Blackmagic Motion JPEG?

What framerate to you use? Have you tried to reduce it to 29.97 or 25?

Have you tried to capture uncompressed video (please note that it requires lots of hdd space)? Do you get the same results?

How much of your CPU is used by your video capture software? 100%?

Some common problems:
Blackmagic Intensity Pro issue: Frame drops caused by codecs and codec packs
The installation of some codec packs can cause media players to drop frames while playing Blackmagic uncompressed HD clips.

Some freeware and shareware codec packs override Blackmagic codecs when playing back uncompressed video. These codec packs are neither designed nor suitable for playing back uncompressed HD clips captured with products from Blackmagic Design.

For this reason, it is recommend not to install freeware and shareware codec packs when working with products from Blackmagic Design. Unwanted codec packs can be uninstalled using the Add/Remove Programs from the Control Panel in Microsoft Windows.

Blackmagic Intensity Pro video issues caused by the performance of your hard drive
Try using an HDD utility such as free HD Tune that allows to show a transfer graph. See if it's nice and smooth or full of peaks and valleys.

Blackmagic Intensity Pro issue: Audio out of sync when recording video game (from xbox 360)
Make sure to capture video with the same framerate that your video game console uses for outputting video. If it outputs 30 fps, then use 30 fps when capturing. If you use a different frame rate, you may try to fix the audio/video out of sync problem with VirtualDub.

You can also record sound from the "Line In" of your sound card instead of capturing from HDMI audio. In the Black Magic Control Panel change the setting for HDMI input and Analog RCA audio. This will allow you to use HDMI for video input and RCA audio for audio. You will need RCA to mini jack cable that will be connected to the "Line In" of your sound card.

And you can file an official support request on the blackmagic web-site