I haven't done any jailbreaking or installation of Siri, but my iPad3 has been doing strange things since 5.1.1 such as coming out of sleep, lighting up the lock screen then displaying the shutdown screen a few seconds later. Without input, it goes blank again a while later. I think, if I did not have a smart cover, it'd keep doing that, cutting into it's battery for no good reason.
And on topic, I just recently shut it down and the bugger won't turn on. It displays the Apple logo for a few seconds, the screen flashes - as in the brightness looks like it maxed out, not turned white - then goes out. A little later, the Apple logo comes on and the whole thing repeats. This happened a few times before I realised it was in a loop. A quick google and saw a short line about someone's iPad only starting up if plugged into the charger. So plugged it in and it started fine. That said, there were a couple of other quirks, like the sleep/wake button was doing strange things as well, like nothing what it's supposed to. Like it was stuck down or something.