The items that do need watching are just a subset of the "old days."
- Maintain your daily backups - probably the most important thing you can do for Exchange
- Examine your message queues for log jams or stuck messages
- Check available disk space (but you've already automated this, right?)
- Examine the event logs for errors and warnings
- Make sure your anti-malware software is functioning properly, i.e. turned on and getting updates (some people host this service, so that would only leave four items :)
Thanks to Jim McBee for providing guidance in his many excellent books.