'Watch'ing You
A stalker's dream come true

Is it possible to eavesdrop on other rooms?

I have not found this to be so, but it could be due to character limitations. I believe it would be a good idea, though, to be allowed to 'watch' in a direction; north, south, etc., or '01' if you would, say, press your ear up against a door to an apartment.

While watch is primarily used in a close setting and allows you to hear minute details of certain conversations, watching a direction could allow you to pick up tidbits of the whole dialogue, albiet not nearly as clear as you might from an in-room watching. This, of course, would all be dependent on your Perception.

I think this can be made fairly balanced, especially with the addition of new cyberware that might enhance your ability to do this, or make you easier to detect. If someone in that  Security Barracks you've got your little ear to has thermovision, you're practically fucked as it is.

Not sure if this is already in place, or what. Any ideas/comments?

Cyberware, yes. But isn't within the realm of possibility to have a minor version of this integrated?

If people in the next room are speaking loudly, you can 'hear voices from the <direction>'.  It may only work outdoors though.. or it may be that I'm the only one who habitually types 'emote loudly' and 'speak loudly' everytime I enter a room with people in it.