That's one reason why I mulch so much, it keeps them down! the quantity of seedlings does diminish with time, as long as you keep on top of the weeds, but they're a major pain. it soon becomes obvious which are the veg, as they'll be growing in a straight line and nothing else will.
Dandelions can be a right pain. they're not too bad where I am now as the water table is close to the surface and they don't need to go very deep. When we lived in Cornwall, we were just above an old clay pit, with the water table way down. Bot long after moving, we had a septic tank put in. The hole was 8 feet deep, and the dandelion roots were still going strong at the bottom, barely thinner than they were at the surface.