I ended up using iTunes to download the movie. And you're right bluedana, it took forever to download! There is an option to start watching the movie while you are still downloading the whole thing. I hit that option and it worked for a couple minutes until an error message came up and it stopped downloading the movie. This happened a couple times, so I decided to stop watching the movie until it was completly downloaded. When you play the movie, it popped up really big on the screen so that the movie was all you could see. That feature was nice. But, from time to time I had to pause the movie. And even though there was a play button on the screen, it wouldn't work when I wanted to resume the movie. So I had to go back to iTunes (i.e. leave the pop-up) and then double-click on the movie to make it resume playing. One time iTunes froze and so I had to cntrl-alt-del to close it. When I opened it back up, I had to log back in to make the movie come up. But it indicated that it wasn't completely downloaded (even though it really already had been completed downloaded), so I had to wait 30 minutes for it to download again.
Today, I watched part of the movie again with no problems. It didn't make me download the movie again in order to watch it (even though I had gotten out of iTunes the day before and had shut off my computer). iTunes told me how long it was going to be until the movie would disappear from my library. When it said that the movie had expired, I double-clicked on it just to see what would happen. At that point, the movie disappeared from my library.
My advice to people is that if you want to use iTunes to rent a movie is to start downloading it a couple hours before you want to start watching it. And, try to avoid pausing the movie!