You're quite right, morgan. Harmonics describe it very well, except the "harmonics" are very closely spaced, kind of like if the harmonics on an organ pipe were spaced mere fractions of a semitone apart. Just like when tuning a guitar, there will appear to be variations in output intensity (beats) when striking very close "chords", so too will there be variations in laser output intensity with multiple longitudinal modes, but the variations will be way too fast for the eye to catch (except in a so-called mode-locked laser, which is precisely like a beating guitar, with strong pulses where the harmonics align and no output between pulses).
If the pond analogy was hard to understand, you can visualize it more simply as a large collection of beams that overlap, rather than a single beam. The important part to "get" is that they do not readily focus to the same point without tricky optics being used. Kind of like the difference between a siege crossbow and a small army of archers: the archers will fire their arrows slightly spread out in time, and the spread will be larger, so while you can hit an enemy force hard (equivalent to the laser heating a surface in a larger spot), you still can't breach a wall (equivalent to the laser focused to a single spot that then vaporizes right away, because of the more massive energy in that tiny point).
Hope that's clearer.