I'd like to understand the security implications of re-using keys across a privatenet, the public testnet, and the production network. If this is bad, why so? Are there advantages or disadvantages to doing such a thing?
It's not recommended to use production keys on non-production networks. Some basic reasons are it's similar to why you shouldn't reuse passwords, or that you wouldn't put $1 in the same wallet as you would put $1000. There is always a tradeoff between security and convenience: whatever is easy to get to is usually less secure. Conversely, if your production key is in a safe, every time you want to test something you don't want to have to go to the safe and get it.
It's also good to be aware of replay attacks, even though replay attacks between Ropsten and production network are prevented if using an updated client.