Perceived flicker can be massively reduced if you can prevent the current from dropping to zero at any part of the cycle. A small capacitor in parallel with the LED will do that quite well. It does not have to be large enough to keep the current anywhere near constant for the PWM cycle.
A lot of LED lights are supplied from a transformer, and some don't have any smoothing capacitor, so there is significant 100 Hz flicker where the mains is 50 Hz. If you calculate the capacitor needed to keep the voltage largely constant for each half-cycle, you end up with a very large capacitor. I have found that the capacitor can be 10 times smaller and the flicker isn't visible.
For instance, if you have some lights that take 500 mA at 12 V or so, it would be normal to have a capacitor that would keep the ripple to 1 V or so. That would need somewhere around 5,000 μF. That is what you would need if you were running electronics that has to take the same current for the whole cycle. With LEDs, a capacitor of 470 μF will usually virtually eliminate visible flicker. Typically the LED voltages would be 8 - 10 V, and a series resistor limits the current. With a 470 μF capacitor, when the supply voltage falls each half-cycle, the capacitor voltage rapidly falls to near the LED voltage, and very little current flows, but the voltage stays above the LED voltage, and the current doesn't fall to zero before the next half cycle.
The dots that Audioguru describes are not visible in those conditions, because even at reduced current, the LEDs continue to emit light, so the contrast between the bright and dark points is far less than when there is no capacitor and the LEDs turn off.