My city composts yard waste and also adds clean unpainted drywall and lumber scrap. The gypsum in the drywall is supposed to help with our heavy clay soil.
Compost operations like this are usually hot so you can expect weed seeds to die in the process. Mine comes very well sifted and I've used several tons with no apparent change in weed population. I say that knowing I have tons of weeds so take it with a grain of salt.
A little trash is inevitable. Screening helps separate that stuff out but in a large operation there is only so much they can do. The plastic bags are likely landfilled and all you see are scraps of torn bags. A couple other things about quality: they probably have a permit from the state to do a municipal compost operation, and it may have requirements for what they can and cannot put in, like painted and treated wood, trash etc. That should be a publically accessible document either from the city or state. Also, they may do tests now and then and post the results. My city does not test every batch but does have a couple samples posted online to give users an idea of pH, NPK, Ca, Mg etc.
I pay $12/ton if I bring my own trailer on a compost sale day. And it's a generous ton.
All in all, it's a great value especially if you need to treat an entire lawn or you're starting a garden area and need to till in a large amount. It's not loaded with nutrients but compost is mainly for improving texture and organic matter, not as a fertilizer. I of course make my own compost so this stuff is not all I'm using anyway.
Close the loop, buy city compost! [Edit: I just noticed your title says FREE. What's not to like??!? I'd be on that like a fat kid on cake. Get after it!