How can I set the time before the screen dims? I've got an iPad 3 on iOS 5.1. When reading occasionally my screen will dim before I interact with the screen; it doesn't turn off and lock but it dims.

How can I lengthen the timer for this? Is it the same option as the "Auto Lock" timeout in the Settings app?
It is determined by the Auto Lock time and cannot be set independently of it. The Auto Lock can be changed in Settings > General > Auto-Lock. The longer you set it to not auto-lock, the longer the display will maintain it's normal brightness.