Recovering from Moles, Weeds, and Overseeding Issues

New to lawn care. Fertilized spring/summer, core aerated and overseeded in fall, got nice grass. Now moles (from aeration?) and weeds (from moles/grubs?). 40% back lawn covered in light green grassy weed, clover, purple flowering weed. In NJ. The expert says moles unrelated to aeration; use Mole-Med. Weeds natural; use selective herbicide, get help at garden center. Tackle one problem at a time.