I let a friend of mine use my phone to access his Airbnb account. He couldn't type in the messages area because backspace kept erasing all the content. There appeared to be other navigation issues as well. Unfortunately I don't have an Airbnb account myself so I won't be able to verify fixes here :/ .
Is the device using the SwiftKey keyboard? Sounds like a dupe of bug 770291.
Sorry, I should have given more info. It's a stock Galaxy Nexus (Jelly Bean) with the stock Android keyboard. It is/was running Firefox (not beta) from the market.
The keyboard issue probably is a dup of bug 770291. The general problem with the site on FF Android likely a layout compat issue for evangelism.
Yes, this does sound like bug 770291.