How can you tell if Curent is Flowing?

[jdurand]

Depending on the LED used, it may not like being reverse biased every cycle. You could use two LEDs wired in parallel but reversed so one lights at a time or put a diode across the LED to clamp the reversed half cycle.

The old, dim, green LEDs are really rugged so are often used in a circuit like this to avoid the cost of the diode. More modern LEDs like bright green and others don't like reverse voltage.