Sure Adobe Remix is cool, but others like Jumpcut got to that idea before. What's needed more is integration of metadata tags, a nontrivial issue which is increasingly attracting investment according to alarm:clock and Mashable.
Ok, it's dying out but with Google video you can tag an URL to go to a specific time (or even add subtitles), for example to access starting at 1 min 26 sec, add #1m26s to the URL. The embed tag would work like this according to Simple Thoughts: [like this sorta] embed FlashVars="initialTime=2171".