The secret ending to Lost In Translation

Bob and Charlotte spend the night together.

The movie is purposely vague about the events of their final night in the hotel, but they leave us a clue:

When Charlotte gets off the elevator (after the fire alarm), they say good night. Bob is still wearing his jacket after Charlotte leaves the elevator. But in the morning, when Bob is looking for Charlotte in the lobby, he leaves her the following message:

"I was calling to see if you still have my jacket, and if you could bring it down, but you're not there, so this is goodbye - and, uh, so, I guess...goodbye and enjoy my jacket which you stole. From me."

How did she get his jacket?

You could chalk this up to a continuity error, but I prefer to think that the movie is tactfully telling us they spent that last night (or some of it) together.

But the real question remains: Did I actually notice something new, or has everyone else already pieced this together?