Corn gluten meal, a relatively new and increasingly popular natural herbicide, appears to be successful at preventing crabgrass and other common weeds. A by-product of milling corn, it is completely benign. Some companies sell a pelletized form containing potash and nitrogen, but you may have to search a bit or ask your retailers to stock it. You can eat their young leaves in salads, and in fact, they were brought to this land as an exotic green. Get a weeding fork.
Dandelions have a two-year life cycle.
When they're in the first year and appear as basal foliage, dig them out with a vengeance. It's great exercise. If you let them go to seed and spread their progeny, you'll have to start the process all over again. Japanese beetle grubs and their adult counterparts are a problem in much of the eastern United States. They cause lawns to turn yellow and die but are fairly easily controlled through nonpoisonous means.