A lot of the weeds appear to be grasses. There is a grass only spray that will not kill broad leaved plants: Grass-B-Gone made by Ortho. The others you'll just have to pull -- preferably before they go to seed. Then maybe the the horseherb will be so thick they will shade out any remaining seeds, but no matter what the groundcover there will always be some weed pulling to do, even in a thick lawn.

Wishing you the best!

Thanks for the tip. Grass B Gone seems to be just what I was looking for.

Is that a flat seed pod I see in the lower right quadrant? Does it perhaps contain 7 or 8 flat, husked seeds? If so, it's probably a form of poa annua, or meadowgrass, which is usually an annual. Those who are learned in such matters say that the most effective control is to put down a pre-emergent in late summer, to prevent the next crop of seeds from sprouting. As for herbicide application, I wonder if mowing everything short wouldn't make it easier to target the base of the individual weeds. Might want to pull off the seed pods beforehand, to avoid scattering.

Funny thing, Horseherb IS the weed in my groundcover, but with a shoe polish bottle with a little sponge on top, full of Round-up, I've about got it all killed out.
Jim

The shoe polish bottle is great idea. I'm really glad I found this forum.

My Horseherb turns from friend to foe as soon as it crosses the edging. I have a feeling I'll be dabbing runaways real soon with an old shoe polish bottle

Horseherb doesn't crowd out other weeds that I've ever noticed! Of course, it's a weed itself, as far as I'm concerned. I was pulling some out of my garden today.