Weird touch screen response in my Nexus 7

My Nexus 7 is behaving weirdly since the last update. Sometimes it behaves as if I pressed something, even though my hands were nowhere near that point. For example, when I am reading a message, the Nexus types a couple of letters, even though my hands were not on the keyboard. I don’t know if this is related, but it also seems to be lagging a bit more than usual. Are there some settings or some steps I can take?
