As has been said, never ever move the X360 with a disc in. Not ever. Not for any reason.
That said, even if you don't move it, if you've an older model their DVD drives can sometimes be a bit dodgy. I had to RMA one, some years back, because it stopped reading discs. And even now it sounds like a hovercraft when running (I just install everything so I don't have to deal with that usually).
In fact, that's a fair point: are you installing to the hard drive and playing from that? If not, do. Quieter, usually much better, and reduces the chance of disc eating.