And if you use a mercury sphygmomanometer, you can actually see those pulses appear and then disappear. (It's harder to see them with a gauge-based one.)

The pulses you see are no substitute for a stethoscope. You see them later and they dissappear sooner than what you hear with a stethoscope.

You need a closer eye on it ;)

Or go slower.

I'm an anesthesiologist; we will sometimes use a pulse oximeter below the cuff as a quick estimate. With practice you can estimate SBP to within 5 mm Hg or so, which is more than enough for our needs.

How about feeling in your arm? I think I can gauge it reasonably accurately.

Palpation BP's are good enough for +/- 10 mm Hg, but not much more, and won't give you diastolic.