Sounds like slugs! They love petunias...I lost a whole pot last year while on vacation.

Rob, are you watering in the evening/night? If so, don't. :)
I had containers of petunias last year and if I watered at night, the slugs were all over them. I stopped watering in the evening and the slugs weren't such a problem.
In a flower bed near the petunia pots, I put a small dish at dirt level and filled it 1/2 full of beer. The slugs are attracted to it, fall in and die.

'Escar-go' or 'Sluggo' are both non-toxic, very helpful slug baits. You can find either of them at any decent garden department.

(Iron phosphate is the active ingredient. Other slug baits are very toxic and should be avoided.)

When I was first building up my garden, I bought and planted lots of plants from the local nurseries. I had a terrific slug problem for many years. One of the contributing factors was that I was importing nursery slugs right along with the plants. Have you seen their plants sitting on the ground waiting to be moved up to the table as a space clears? If not at the nursery itself, then at the wholesaler that trucked them in. That's how slugs can get into hanging baskets. That mistified me for years.

Wow....cool. Glad I read that. I have been scratching my head for weeks trying to figure out first WHY there were holes then after discovering it was slugs ..HOW the slugs were getting into the hanging baskets of trailing petunias I have. I sprinkled some "slug stuff' I bought at a local home improvement store around the base of the pole. THEY were still there! Drove me insane. Do you think I could put the slug medicine stuff into the hanging basket to get rid of them?

I use, used coffee grounds. I get them free from our local coffee shop. Or use them from your coffee pot. We're not big on coffee, usually only one cup each. I use it on my hostas, and petunias. It makes the yard smell good too. I just sprinkle it with my hand around the bottom of the plant. It works great.