In reaction to your request for non-toxic weed control. You have to realise that any weed problem is usually a question of imbalance in the soil.
Weeds are there to restore the balance inyour soil.
This might take a couple hundreds of years, so you probably don't want to wait that long. To correct this imbalance all you need to do is applying the right fertiliser. Broadleaf weeds are usually an indication of Calcium deficiency and one or more of the trace elements.