I played around with this a title more today testing out keyboard shortcuts.
If you press Fn + F4 (4) it will shut off the screen on both the lapdock and the Droid, its basically the equivalent of pressing the power button. Ctrl + Alt + Del (Fn + Backspace) will reboot the phone. Ctrl brings up settings, Esc will work similar to the back button IIRC, and Fn + Home works as a home button.
The speakers will work even with the lid closed so the lapdock can be used like an audiodock. They aren't the best sounding since they are small, but still an improvement over the little built in speaker and since there are 2 of them on the dock you get stereo.
Remote RDP is a nice Android app that supports mouse input and works using the lapdock, meaning right click and left click work and you only see one cursor, but you'll have to configure this in the options. Unfortunately you are limited to using 960x540, even though the lapdock screen can do more you are limited to the Droid 3's resolution since its being mirrored.
Motorola Droid Bionic
Stock 4.1.2 Rooted
CM11 4.4 Safestrap