Things that go mmfffbt, thump, bump in the night

As I mentioned in my catch-up post.  Two of our neighbor's cats have chosen to reside with us a majority of the time.  We recently had two cat doors installed, one to the garage, the other from the garage to the outside so we won't have to let them in and out manually when it gets too cold to leave the sliding door cracked as we do now.  In one week's time they were trained, and one of the cats uses the doors regularly, seeming to enjoy the independence of coming and going as he wishes.
The other is less enthusiastic, seeming to feel that as his staff, we are shirking our duty if we don't let him in and out the sliding door.

The other night, we had just gone to bed when Thing2 said, I hear some muffled meowing, I think he brought something in.  I got up and looked, and all I saw on the floor in the living room with the cat was a feathery cat toy.  But then Thing2 came and looked, and saw it.  A mouse.  It was alive, but not moving -- all legs out.   I got a towel and carried it outside and put it in some bushes, and once it was safely in the towel, it did move -- maybe just playing dead earlier.
Two nights later, a racoon came in at about 5AM.  I knew we were going to have to close it down at night, but I was hoping we would have a little longer before it was a problem.