There should be rules which notify them if something is anomalous, by email, SMS, or logging a problem on an incident management tool. e.g. "Java request foo.bar() on Managed Server 1 is throwing exceptions for 50% of invocations (20 requests, 10 exceptions) in the last 10 minutes. This affects the following services: Customer Login page on foo.bar." possibly even attaching some of the exception messages to the email, if sampled through instrumentation or correlating it back to the log files, automatically.
This type of monitoring is actually useful because Ops understand what is broken, what it effects and gives them enough detail to either fix it or pass the problem to someone else; and they're not wasting their time looking at graphs waiting for a problem to appear.