An awful lot of grease fell into the bottom of my oven during its last use. Afterwards, it made sense to use Dawn to clean the oven, as it cuts grease so well. After I did that, however, I thought to worry about any ill effects of heating the oven. I did go over everything with a wet rag several times, and believe I got all the Dawn out.
Specifically, I used ultra concentrated Dawn dishwashing liquid which has no phosphates and which carries warnings to not mix with bleach. So, do I have anything to be worried about?