When you spread your compost, you will be seeding your lawn and garden with seeds for the coming year. Rodale's book says that you can compost them if you carefully monitor the pile where they are to ensure that the temperature gets hot enough. Over 140 degree temperature is required to kill most weed seeds. It is safest not to compost them. Send them to the municipal recycling site.
Weeds spread in different ways.
If you think about the way that a weed reproduces, it will assist you in your decision as to whether or not to put it in your pile. Also consider that if you are not building a hot compost pile, live weeds will probably continue to grow in your pile. Experts disagree as to whether the weeds' ability to reproduce is destroyed by the heat of the pile, but they all agree that hot piles are not uniformly hot. If you have any doubts about a weed, don't include it. It is not worth seeding your garden with weeds as you spread your finished compost, then finding out you were wrong.