Should I stir up my compost?

On the subject of cardboard you can put in most domestic packaging, however there is as with most things a ' but', don't put card board in that has been in contact with the food stuff. A good example is fish finger boxes.  I also tend to avoid the packaging that has a glossy finish.   Breakfast cereal are ok as they have the inner bag - check that no one is collecting the 'vouchers' that are often printed on them!!

One of my older Alan Titchmarsh books ( 1991 ) says that turning the compost heap is not necessary , other sources advise turning.

Composting is a fascinating subject and you will hopefully be pleasantly surprised at what you can put in. There are books available devoted to the subject.   

First I would check how the rat has been getting it.  He's unlikely to leave voluntarily unless you make conditions difficult or unpleasant for him e.g. block up the holes and put weldmesh underneath the bin, if he's been tunnelling in (this will depend in part on the design and materials of your compost bin).

Yes, rat's urine can contain lots of nasties.  That being said, when I had a rat in my bin I simply blocked up his entry hole and then forgot all about it and used the compost once it was ready.  I'm still here ... 

I doubt there are many compost heaps that don't get visited by rats, they urinate constantly so 'contaminate' everywhere they go.  The main risk is Leptospirosis (Weil's Disease). However, there are only about 40 confirmed cases per year in the UK and generally only produces flu like symptoms. It can also be caught from cattle urine so using cow manure is a risk factor too. Just as likely to catch it from water in rivers and lakes as from the rats in your compost. Make your own choice.

Yours was probably trying to nest in that nice warm environment you have conveniently created. Rats suffer from 'novaphobia' (fear of new environments) so if you move things around they may go looking for a home elsewhere.

Remember "you are never more than 164ft from a rat" http://www.bbc.co.uk/news/magazine-20716625

I agree with trikidiki, keep kicking the bin. You could also try taking the top off, if it gets rained on they don't like it also.

In order to get rid of things that vermin like, I'm using a Bokashi bin. It "pre-composts" everything including the stuf that you wouldn't put in a compost bin like cooked food and meat, then you bury it a couple of feet down and it vanishes completely. It doesn't smell because the bran that you put on it is innoculated with fungi that absorb the smells. It works well for us, no food waste goes into landfill anymore.

I've put bricks in front of the holes... so far, so good. Will check over the next few days that ratty has now been deterred.

Interesting what you say about Leptospirosis, Trikidiki.