THE UNDESIRABLE!
WHAT TO AVOID COMPOSTING
Plants planted as seeds and the fruits of certain trees or shrubs (hornbeam, etc.) because the seeds do not decompose until the compost reaches a temperature of 60 °. Otherwise, you would scatter unwanted plants with your compost there.
Coal ash: they are too rich in mineral salts and have a herbicidal effect in the compost.
Practical guide to composting
Consumer-durable / how well-composted waste-its-t3892.html
ps: for a little while I have been wondering about the methane released, under certain conditions, by some (large) heap of compost ... at the greenhouse effect level wouldn't it be worse to compost than to incinerate?