I have no knowledge about what Circle did during the downtime, but I can talk as a Clojure expert.
> Is there a way to automatically identify the diffs between your codebase and what's running in production?
In general, no, because Clojure functions aren't serializable, so it's not possible to get the source for a running function in production. There are hacks [1] and approximations [2], but I'm not aware of anyone running them in production.
> Or did you just review repl logs to see what had changed?
Logging the REPL is possible, but it is far easier to do client side than server side, meaning every dev would have to have it installed, and it's easy to "circumvent" by e.g. SSHing into the production box and running a repl in the SSH terminal. (I don't mean circumvent negatively, just that 'install this tool on every dev IDE and use it at all times' is a somewhat fragile process during a firefight).
Also, the last time we investigated REPL-logging, it was too verbose to be convenient. Most nREPL tooling evals a significant number of expressions to e.g. grab docstrings and function arities, so it's hard to isolate the actual changes made. The difference of a single keystroke is also the difference between "eval this function" and "eval this entire file". If the developer evaled the file, you'd then need to diff the string buffer that went over the wire with the committed file, rather than just saying "oh, Alice eval'd this one fn".
If you have live-patched code that you want to keep, the simplest solution is just push it to production as part of your normal deploy process and reboot all servers, so they're guaranteed to match the committed code.
[1] https://github.com/technomancy/serializable-fn
[2] https://github.com/gtrak/no.disassemble