I had the same problem too! I downloaded 7 rental movies for a week's fishing trip in France (NO internet connection for the week). Started playing the 1st one on the first night there, and it seemed just fine. Stopped the film halfway through, and when trying to start it again later that evening, got the dreaded "cannot open" message! Tried all the other films (including the one I'd already started to watch), and got the same "cannot open" message. None of them worked for the entire trip. When I got home the following week and connected to WiFi, they all started playing just fine. Turned the iPad to airplane mode, and started getting the error message again.
I opened a case with Apple Support (who have refunded the payments for all 7 movies) and they're trying to tell me it's a download issue! I'm not so sure - I think the movies are all downloaded just fine - but it seems to be some sort of validation issue requiring internet connection (though, if that's the case, I don't know why the one I'd already started to watch was giving the same error message when I went back to complete it!??)
On their latest support email, they've said the following....
"when you download more than 2 movie rentals at a time they will not be completely downloaded and will not play completely and will show the message "cannot open", therefore I advise you to whenever you download movie rentals always download one at a time"
I'll try this next time, as I did download all 7 rentals at the same time, but I'm still dubious that it's a download issue as I've definitely downloaded multiple rentals previously, and not suffered this problem before