Though it would not have saved the day in this instance, it would be a good implementation. So many times I do not want all my apps alerting me with push messages and emails and texts; I just really want phone calls or alarms to come through.
As for this article, there seem to be conflicting expectations. Demanding attention is the point of an alarm, so I for one do not expect "mute" to imply "and cancel all my meeting reminders or let me oversleep". Another comment proposed a theater mode, and maybe that should mean "no noise whatsoever for the next N hours, warn me if it means deferring an alarm".
It's called off. Hold the top button and the home button and you'll get a screen that lets you power off the iphone completely. To turn the phone back on just press and hold the top button for a few seconds. :)