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Choose grass seed to match your situation.
The best cure for weeds is to mow regularly. Any pesky thistle/milkthistle/dock can be individually lifted. If mossy then use a moss controller and rake over. Raking sand in, a little at a time will improve drainage, and gradually level. In the winter fork the soil to aerate. -
The grass will suppress most weeds. Mowing it regularly, as @rive_gauche suggests, gets it to grow vigourously and it'll soon see off anything else. Grass has evolved to respond to being eaten by grazing animals, so mowing it stimulates that response.
Thanks guys. Goal is to have a nicer lawn, really. A lot of it has grass, just also lots and lots of weeds. I'll do what you've suggested on the bald patch, Andy. The rest, however. I'm not huge on the idea of coating the lawn with chemicals, but is there a particular weed killer that would leave the grass alone?