Aphids are tiny pear-shaped insects that spend most of their lives in the same spot. They feed by sucking the juice from basil leaves, leaving unsightly spots. The leaves may yellow and become distorted or drop off. Spray with insecticidal soap, paying particular attention to the undersides of leaves and the point where the leaf joins the stem. Insecticidal soap doesn't kill eggs, so several treatments may be necessary.
Japanese beetles are dark-colored beetles with a metallic sheen. Their larvae are lawn grubs. They skeletonize leaves by eating the soft tissue and leaving the veins. Both Japanese beetles and their larvae are difficult to control. Control a few beetles by hand picking. For more serious problems, control the grubs using Bacillus thuringiensis (Bt), nematodes or milky spore. Choose a product labeled for Japanese beetle grubs and follow the instructions carefully.
To see if slugs are the culprits, watch for their slime trails and check the plants at night with a flashlight. Hand picking is effective, but wear gloves because slugs carry diseases. Garden centers carry several products to combat slugs.