Seeds may sprout, usually indicating that your compost did not get hot or stay hot long enough. For some weeds and in some situations, this may be a problem. But in other situations, it may not. As with most
permaculture answers....it depends.
I never turn down seedy weeds or grass clippings because my compost bins run hot, killing most seeds. Some survive, but not lots and lots. I can deal with them. If I avoided seedy material for my compost, I'd be turning away 2/3 of what I make into compost. I'm not willing to turn that stuff away, so I've learned methods to work around it.
Second, most of my garden beds are mulched. So most seeds can't germinate through the mulch layer.
Third, of the beds that are not mulched right away, I will lightly hoe or flame once a week. This kills emerging seedlings. Done once a week is light easy work. If left to every other week, then it's labor and I don't consider it fun. The trick is to lightly scratch or flash burn the surface when the seedlings are just emerging. This type of weeding goes quickly.
Once I harvest a crop, I remove any surviving mulch for a week or two before starting again. (note: if the weather is hot and dry, I'll sprinkle a very light covering of grass clippings so that the soil surface doesn't bake dry.) This allows many seeds to begin sprouting. I then prepare the bed for the next crop by applying a fresh layer of compost which I till in. The tilling kills any emerging weed seedlings.
My hugelkuktur pit growing areas are a different situation. They are essentially giant cold composting pits (although in actuality, they get warm). Again, I don't turn away seedy material. But as weed seeds begin to sprout, I simply cover them up with more material. Sometimes I don't have more organic material on hand, so I use the flamer to kill off the tiny emerging weeds.
If I didn't have weed control on my weekly job list, then perhaps I wouldn't put seeds into my compost bins. But I've developed a solution that works for me, giving me access to lots of seedy organic material that other people turn away. I run 30 one cubic
yard compost bins, so those bins are always hungry for more composting materials, seeds included.