Peter,
It's tough to quantify exactly for all situations but I'll give you 3 examples:
1) If the mostly gently stroked putt from3-15 feet in length is in danger of going off the green if it misses, then something's wrong.
2) If a putt down a slope is simply impossible to stop within 2-3 feet of the hole even if it is just barely trickling along as it starts down the slope, then something's wrong.
3) If a sidehill "rainbow" putt will be going so fast as it starts to break sideways that it is impossible to to stop it within 2-3 feet of the hole, then something's wrong.
I see it often on Bent Grass greens that were built pre-WWII; they weren't designed for today's Stimp readings, they were designed for pre-WWII green speeds. But nobody wants to "restore" that part of the original design.
These days, clubs seem to want to have ultra-fast greens for the same reason that a male dog licks his testacles - i.e. because he can.
Clowns' noses and windmills.