Physically, the external monitor was to my left. However, by default, the MacBook thought it was to my right. Then, I discovered that, in System Preferences->Display, you could rearrange the logical position of the screens to match the actual physical configuration. After correcting the logical positions, everything went smoothly and behaved as expected. I could move the mouse pointer from the MacBook’s screen to the external monitor seamlessly. I could then move some windows over to the external monitor as well.
Spaces worked fine too, giving me additional workspaces on the external monitor as well. I could also move the Apple menu bar to the external monitor if I wanted to.
It would be interesting to have a 30″ monitor that displays 2560×1600 pixels. It requires a $99 mini-DisplayPort to dual-link DVI adapter though.