But suppose you miss some weeds that are starting to flower but the flowers aren't open yet? I think most growers will just pull or cut the weed and leave it in or near the field.
I want to show you a time-lapse video I took. I cut the flowering stem off of an annual sowthistle plant and took a photo with a special camera every minute for 6 days. As you can clearly see, even though the stem was no longer receiving water or nutrients from the soil, at least the flower bud continued to mature and produce seeds. Now, having said that, I have not germinated the seeds to see if they are viable, but there is a good chance they are. Click HERE for video. It's about 1 1/2 minutes long, but most of the action happens in the first 50 seconds.
So the take home message - if the weeds have flower buds starting to open, remove them to covered piles, trash cans, or other area where they will not be a source of new weed seeds.