This is a bit like the old question "Do you still beat your spouse?".

The more pests, odors, and problems your compost piles have, the more questions about one's composting competence and knowledge might be asked.

I found a nest of mice in one pile during early spring. And a few grubs once.

I don't want to think it, but perhaps -- just maybe -- there is a possom on the property who thinks he/she might have arrived at Kitchen Scrap Heaven. My compost bin.
Don't know for sure, but I suspect.
Sunny

My two persistent visitors have always been mice and grubs. My piles are riddled with mouse holes (strangely, this may be good for aeration of the piles and the fact that I have caught very, very few mice in my traps in the house) and when I have chopped into the piles and run the aged compost through my screen I have noted large (3/8"-1/2") tunnels that I have assumed to be grubs.
I am in KS, USA and also note a crop of "green" June bugs in early summer around the piles...
Hortster

Last summer I had a ridiculous amount of soldier fly larvae in my compost. The neighbor worked at a restaurant and would come home with grocery bags of day old bread. What we couldn't eat went into the compost. It heated things up pretty well, but scores of soldier fly larvae appeared shortly after. So many that the surface of the pile appeared to move. It didn't bother me, but the lady friend who hates anything squirmy wouldn't take out the compost while they were there. Luckily (unluckily?) the neighbor got another job and the bags of bread stopped coming. I haven't seen soldier fly larvae since. She takes out the compost again, too.

BREAD??? Don't let Annpat see this post.
Otis

I disturbed one fat, healthy looking mouse in my pile last week when I turned it for the first time in months. He ran up onto the top of the next bin over, looked at me for a second, and took off.

I had a vole who lived behind the bin for a little while last summer. I would see him when I turned the pile. He was there for a month or so, then he was gone.

the mouse that looked at me for a second didn't make it---the shovel found it and now its composting with the bread........

Twice in 12 years we had a bear throw the pallets that make the compost bin several feet and there was a nice big bear print in the soft finished compost. I don't think this reflects on my "composting competence and knowledge" in the slightest. We live in bear country and they pass by our house periodically. In the winter I cold compost and the bear woke up looking for food earlier than I turned the compost. Twice in 12 years isn't bad. If it happened twice in one year I might think about changing my method.

We don't have skunks, raccoons, or possums here and there's been no evidence the mice, coyotes, foxes, or other critters ever bother the compost. The squirrels and grey jays sometimes visit but I don't think they eat much in the compost as we feed them sunflower seeds. ;-)

Something bent in the side of my wire mesh circle this week. It was probably a raccoon. Too many big kitchen scraps. I added a lot of sawdust and composted manure today and mixed it up. But the visitors don't bother me. Just NO soldier fly larvae (can't even say the "M" word).

Any of these could have visited my piles, seeing as how all of them have been spotted in or near my garden: feral cats, groundhog, mice, vultures, other birds, squirrels, coyote.

Overlooked that part of the question....sorry! What happened? Some of the stuff in the piles got eaten -- pumpkin seeds and innards, meat, whatever was left in shrimp shells, etc. Stuff got tossed around, and on the grass. And I got to watch wildlife. Yesterday morning, we saw a fox and a flock of about 18 wild turkeys. All outside the deer fence, happily. Very cool, regardless. It's the first time I've seen the fox, which apparently lives with its fox friends down at the end of the road somewhere.

Busload of grade 3 kids from a local school, they asked a bunch of questions and generally annoyed me but they were harmless.

Not what you meant eh? Saw a rat jump out once when I was turning a windrow with the tractor. This was right after a load of stuff came out from town with numerous bags of apples. Do rats eat apples? Jumped off the tractor, grabbed a fork and chased him across the field till I got him, now it's in the windrow permanently.

I hate rats!

Lloyd

A bunch of butterflies came over last summer after I threw in some orange peels...

My chickens usually visit the pile when I let them out to range.