Hi James,
I don't think I've ever seen that on a tomato before. Well, the bug is a Katydid nymph. It is mostly known for eating leaves of plants. The tomato looks like it split and then browned but then there is what looks like to me a white mold or mildew growing also. This is often caused by over watering, as Bubbles said.
Like others said, you might have other issues such as stink bugs that will inject your tomatoes, causing them to get soft spots and rot.
p.s. Watering at night will also cause mold and mildew, especially in our Texas humidity. It's best to water in the morning or just as the sun goes down.
