Sorry if I'm teaching egg sucking, but being new to the iPad, I regard every new trick with awe.
My latest discovery is to occasionally hold the main on/off switch. i.e. the one on the edge of one corner, and the 'home' switch on the face, down for 3 or 4 secs simultaneously until the gadget shuts down and has to be re-started. This apparently "re-sets" the iPad far more comprehensible than just 'swipe to power off' and gets rid of a lot of crap.