Please be aware of the movie rental's time limitation that you have 30 days from the time of rental to watch your movie, and once you start watching it, you have 24 hours to finish watching it. You may watch it as many times as you like during those 24 hours. It may be helpful to make sure the download completes successfully before you begin watching the movie.
Once the download is complete you can watch it without an Internet connection. However, an Internet connection to the iTunes Store is required to authorize playback or activate the 24 hours time-limit of movie rentals. This means, only during the starting of the movie. Once you have started playing the movie rental, internet connection is not required. You can play anywhere without internet connection.
For more information on movie rentals, you can visit:
iTunes Store: Movie rental frequently asked questions (FAQ)
Note: 24 hours time limit is for United States customer only, while 48 hours for other countries.