I've heard of them being very clever and innovative, but can't seem to find many examples. Of course I know about the Hanging Gardens, but not much else (and that is a bit more of an architectural feat rather than cleverness).
The city of Babylon was a center of culture, learning and government for centuries. Which Babylon are you asking about? The Old Babylonian Empire, the Neo Babylonians, or are you asking about the city of Babylon, that existed under the Akkadians, Assyrians, and Persians?
Here are some quick examples that spring to mind:
If you are looking at the wider Mesopotamian influences to civilization, there are many.