The stuff I get has cooked so hot acorns and palm nuts are mush. I have never had a weed problem with it. There are bits of broken glass and pieces of plastic, but my yard is worse in that regard so I don't care.

Cool nil So do they heat it up or do they cook in the sun?

City mulch is usually ground or chipped tree trimmings, so it has not only bark but the inner, more green, nitrogen-rich parts of the trees.

It heats up & composts all by itself.

I don't think I'd mix mulch into the soil, just put it on top.

It may have both, depending on what was chipped. I recently saw our cities forestry department cutting a seed lade Tree of Heaven, "Ailanthus altissima" that could produce a number of new trees of this "weedy" ands invasive tree. However, at this time of year any tree cut and chipped will have green leaves mixed in and that will cause much heat to be generated which could kill those seeds.
The quality will be just what you pay for.

LA also mixes in zoo poo to heat up the pile.

Thanks, all the heat and chemistry of this whole thing is really interesting. I'm going to give it a try.
I've also heard a neighbor mention not to put certain types of cacti and palm in the green bin because they could reproduce. But maybe that was just a rumor.
Sounds like the heat will take care of most of this stuff?

There is a difference between mulch - in this case shredded yard waste - and compost, which has been aged and allowed to decompose. I am not clear on exactly what product you are getting. As suggested, don't till in shredded wood that has not completely broken down. It can rob the soil of nitrogen while it decomposes.

City mulch and compost will vary in composition and quality depending on where you are at. My city offers both mulch and compost, and the compost is tested now and then and results posted on their web page for all to see.