Honestly, it has never really bothered me much. Whatever is in the wood is going to be burned to ash by the time I use it up and my food doesn't touch the wood directly. I don't use the wood inside the house so it's not really an issue. We have a small fire pit that we cook on occasionally and a very small wood pile.
If you use the wood for a fire in the house, would mouse urine or other things like that present any health hazard? Or it just a hazard to those people who are carrying the wood into the house in order to burn it?
There is no danger to you if you are burning the wood in the house. Mouses and other rodents like to hide out in wood piles. I don't cook directly on the wood either (outside). I have never had a problem with anything I have cooked. I'm sure there have been a couple of rodents rummaging through my wood piles. We have over 55 face cord of wood!