There's a "Shop" button on the top right of the Video app (at least there is now) that sends you to the market website. I just rented a movie and it showed up in the "My Rentals" section of the Video app.
Same here first a few time would not update. Shutdown my xoom and rebooted and try updating again. After a couple of time it updated. No video tab on the market yet.
There is no video tab on the regular market, but if you click on shop inside the video app it takes you to the market where you can rent videos. Also has a tab for apps and books.
It took a couple of tries but it finally updated. It is an app that is a player for android market videos and your own downloaded content. It shows you popular content and takes you to a web store where you can rent movies. Now that I have it I can "not rent from Google"
I updated the video app on my 3g Xoom this afternoon and it works fine. It is exactly like the Books app in that it displays what relevant files are on my device and shoots me to the Android market when i want a movie. It works great and streamlines flipping through the marketplace.
My Movies tab showed up in the market as well. I do however think the "rental" prices they are charging are obscene. $3.99 and $4.99 (HD) . This will be something I ONLY use if traveling and I have absolutely nothing else to do.