What bug is causing this and how can I get it to stop?
The symptoms in your photos show fungal or bacterial leaf spots. As these dry out and turn brown the leaf material falls away leaving holes.
Keep leaves dry when watering, and use a fungicide spray labeled for flowers when spots first appear. Fungicides such as chlorothalonil, mancozeb, or copper can be applied to prevent leaf spots. Always read and follow,all label precautions. Do not work in the plants when they are wet as this spreads the fungus. This applies to all flowers including zinnia and black-eyed susan. Here are some articles to compare with what you see--
On your poppy, they sometimes have aphids or slugs. Aphids are controlled by a strong spray of water to rinse them off- they cannot climb back onto the plant. Slugs can be trapped on the ground, overnight, in moist rolled up newspapers, or spread diatomaceous earth or a slug control product beneath the plants. Also the occasional rabbit, deer or groundhog will bite off flower buds but not eat them. A hot pepper based spray may discourage this- reapply after each rain. Poppy does not like wet soil, so perhaps this wet spring caused the browning leaves- check the roots for symptoms of rot- black mushy roots. Sometimes poppy gets bacterial blight on leaves. If yours seems to get leaf spots and begins to yellow or brown before flowering next year, take pictures while it is still changing color, then send pictures, leaf and stem samples to MSU Plant Diagnostic lab for diagnosis. See https://pestid.msu.edu for instructions and the fee schedule.
If you can take pictures of the insects you see, I can be more specific on controlling them. Here are some references that discuss repelling insects on flowers-
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