You'll see extra discrete instances of your finger, as though lit by a strobe light.

This is how we used to be able to measure speed of spinning objects too. :)

Maybe not, but if you do it hard enough while listening to some terrible music, you'll have replicated my 90s clubbing experience.

With a continuous (non-flickering) light you see your blurred finger. With a flickering light, you'll see your blurred finger with gaps in the blurring. This effect is especially pronounced with sharp-flickering light (like in LEDs) as opposed to gradually-flickering light (as in incandescent bulbs). CCFLs are somewhere in the middle.