When viewing a video as part of the page, playing and pausing can be done with the space-bar on the keyboard. When going to full screen, the player no longer reacts to pressing the space-bar. Pressing Escape works like expected though.
Edit: This seems to be a "security" limitation in Silverlight, not the player itself.
When a Silverlight plug-in is displayed in full-screen mode, keyboard events are prevented from being passed to keyboard event handlers in the application. The only valid keyboard input that is acted upon is the set of keystrokes that return the Silverlight plug-in to embedded mode. This limitation of keyboard input during full-screen mode is a security feature, and is intended to minimize the possibility of unintended information being entered by a user.