Earlier quoted context omitted.
Holy shit that's brilliant. I admittedly haven't been to Youtube in forever, but that actually got me to click, if only to find out how (other than altering the querystring by hand) you did it. I still didn't see how to do it though. Is that a logged-in option perhaps or am I just missing something?
When you are at the time you want, right click on the video, and copy the link with the time. "Copy video URL at current time" That's all there is too it :-)
Another alternative is http://youtubetime.com/
But I just modify the query string by hand. :-)