StreamOps tells you when something happens to your streams, in the Notifications page and as pop-ups in the dashboard. You can filter them by level: error, warning or info.
The serious ones are emailed too, so you hear about them even with the dashboard closed: a stream that keeps crashing or won't start, a missed schedule, a YouTube broadcast that couldn't be recovered, and a failed payment. You can turn email alerts off in Settings → Preferences.