Okay I installed the Home Screen Settings application and tried all the different settings, but it still seems to be broken. I am able to lock it into portrait mode for all applications. This makes everything work in portrait as well as lets me swipe down to close. But, any of the other options leave it the same way. For now it's a temporary fix because, in general, I tend to use my phone almost exclusively in portrait mode. But, I would like to figure out the underlying problem here and fix it, as I do occasionally use some applications in landscape mode.

Is it possible the accelerometer in the phone broke? I saw a thread for the N900 about checking to see if it is working, is there a way to do this for the N9 as well?