We're used to mice plagues in Australia. The usual solutions all have the problems that have been listed here, but one of our relatives developed a perpetual mousetrap for his farm.
His consisted of a vertical steel drum, top cut off and half filled with water. Any size will do, but he used something in the 5 - 10 gallon range. You then place a stick horizontally on top with one end in the centre over the drum / water and the other end anchored out past the edge of the drum. You then place a ramp from the ground up to the drum edge end of the stick. The drum can be placed in a bit of a hole, so that the ramp is flatter. The ramp end of the stick can be fixed to the ramp to anchor it. A glass milk bottle is then slid over the end of the stick, so that it is supported horizontally with the neck towards the drum edge and the bottle's bottom end over the centre of the drum. A piece of cheese is stuck on to the milk bottle's bottom edge which is uppermost and above the centre of the drum. You then oil the milk bottle. Nice thin, slippery oil.
Mouse smells cheese, walks up ramp, walks along milk bottle, slips off and falls into water below. They can only tread water for so long. No need to re-set each time, just replace the bait occasionally, if it dries out, and empty the drum if it fills up (which doesn't usually happen, except in real mouse plagues). You won't kill the kids, dogs or the other wildlife either and no cat to feed.
Milk bottles may be hard to find these days, but any glass bottle or jar which is the correct length will do. The concept can be played with, but that's it at it's simplest.
I hope I've described it well enough and I hope that helps you chaps.
Cheers,
Lance