Hi Bluebell, I have composted literally everything in the past apart from diseased onions. I obviously would not compost japanese knotweed but thats another story. I would certainly compost; couch grass, nettles, bindweed, docks, thistles, ground elder, mares tail, etc. The thing is quite a lot of the pernicious material inc seeds and roots, dies off in the process. The composition of your compost is probably relevent, I use quite a lot of comfrey and alfalfa. Of course the more pernicious material you incorporate, the higher the risk of re-introduction but regular weed management is the answer to that, either hand weeding or shimming. Eventually you will compost less and less of the nasty stuff but don`t worry too much, just keep on top with a regular weeding strategy.
Cheers Pete 