The challenge is to remove those weeds during our cleanup efforts and not create a seed bank for future years. Weeds that are bi-annuals will have only grown the rosette of foliage for this year and pose no threat if dug up and put into the compost bins. Perennials like the dandelion are still flowering and setting seed. If you are digging those up, do not include any flowers if you are composting. It only takes a few days for those yellow blooms to have viable seed. Annual grasses with seed heads pose another risk of being spread around. The plants themselves are fine, cut off and dispose of seed heads. Foxtails are the most commonly found grasses in the beds. They seem to like growing up through the center of iris and daylilies where they remain camouflaged among the flower foliage until we begin to see the seed heads. If you are hoeing or pulling weeds with seed heads, be careful to get them out of the garden beds and dispose of them. Since most gardeners do what is called "cold composting" the weed seeds are not destroyed if put into the compost bin.
As the cleanup continues and you are adding to the compost with green parts of our perennials along with the brown spend seed heads and flower stems, the more we can cut those up into smaller pieces and mix them together the better the compost pile will work. You need both the green and browns to get the compost pile really working. If you are pulling weeds, do not worry about the soil attached to the roots. That soil has the decay organisms that are needed by the compost pile. If you find yourself adding a lot of foliage, then add a shovel full of soil every so often. Browns can also be mulched up leaves bagged by the mower. If you need more soil in the mix, use a shovel full from one of your beds as you fill and mix the compost bin.