"If you want a quiet oncall rotation, it's imperative to have a system for dealing with things that need timely response, but are not imminently critical." This is an excellent point that is missed in most monitoring setups I've seen. A classic example is some request that kills your service process. You get paged for that so you wrap the service in a supervisor like daemon. The immediate issue is fixed and, typicall…
Re: this will be a problem soon? Metrics trending. Look for changes in your metrics to spot potential problems and plan for the future. This is done quite often for example in QA to look for issues between releases, and can be done both macro and micro in terms of continuous delivery services' metrics.
The subcritical alerts I think of are more things like "Well, the database is _getting_ full, but it's not full yet." Or to borrow someone else's example, "we put in this daemon restarter when it was dying once a week; now it's dying every few minutes and we're only surviving because our proxy is masking the problem but soon it's going to take the whole site down."