can I rent a movie from iTunes and download it for watching later on a plane?

Yes, movies download, and can be watched later. The clock on the rental starts from the time you rent the movie.

When you download a movie, the rental time starts from the first time you start to watch the movie...If you rent it, it will download and you can transfer it to your iPad....When you start watching it, that is when your rental starts.

You can keep the movie for 30 days, or until the viewing time has expired. Once you start viewing it you get 24 hours to watch it as many times as you like (48 hours in some countries).

There is some debate as to what is required in terms of WiFi connection. Of course you need one to download it. My understanding is you then need a connection when you first start to watch the movie to get the timer going but you can continue to watch it without a connection.

Limnos, once the movie is fully downloaded, it can be watched without any need at all to first connect via wifi. i.e., no connection is required once the movie has been downloaded. I've watched movies at 33000 feet without needing connection to get anything going.

iTunes Store: Viewing and downloading HD content on iPad - http://support.apple.com/kb/HT4095 > Movie Rentals on iPad > * An Internet connection to the iTunes Store is required to authorize playback of movie rentals.

or maybe that's just for HD?

Maybe just for HD content? I must admit I haven't downloaded any HD content recently.