I did most of my section hiking in the off season when thru hikers were typically elsewhere on the trail. Usually we would have the shelters to ourselves or occasionally weekenders or SOBO's. The mice and varmits were far less noticable. Pure speculation on my part is that the mice and other varmits tend to multiply when the food source multiplies as the surge goes through. When we did get on the edge of the thruhiker "surge", things could get less pleasant on occasion usually due to a sense of entitlement expressed by a small but vocal minority of thru hikers. I also observed that there is some sort of shelter manners do tend to get developed as the surge stretches out and the nights on the trail increases.
That said, some of the shelters are just plain old, beat up decrepid places that are best avoided. PA had its share, which I attribute to the easy access from roads and partying which probably leads to the local clubs not wanting to make them nice. Unfortunately that frequently applies to the privies also.