What tools do you use to monitor applications and business-specific data? (apart from Jenkins)
We use Datadog, with metrics pushed from important operational processes using the statsd protocol ( http://docs.datadoghq.com/guides/metrics/ ), so we aren't too deeply tied to Datadog on the application side.

In Datadog's interface we can then configure monitors to alert on any number of things, including anomaly detection if defining thresholds is impossible.

So for instance, we have many tasks that run on a hourly basis, they'll post a datapoint to a given metric (app.task.task_name), and we will then monitor that this metric is consistently posting at one data point per hour. If the rate changes, we get alerted.