Electronic – Purpose of Resistor – comparator

Olin is right about the problem with C23: it lowers the bandwidth of the positive feedback rendering it useless. Just decoupling the supply close to the divider will do the job.

In fact, that is probably also the reason why TI wants to keep the feedback resistance low in value. If the value is too high, the input capacitance of the op-amp alone will already lower the bandwidth of the positive feedback, so on a noisy signal the hysteresis will not work. Normally you would like the hysteresis to be faster than the response of the op-amp; this will be probably be the 510K TI talks about.

If you make sure the highest (noise) frequency that can reach the negative input will be lower than the feedback response, you should be in the clear; however, making the feedback faster then the op-amp can react will be the better option.

Keyword is capacitive reactance. Capacitor is used instead of an actual resistor to avoid heat loss. 1M resistor is only to discharge capacitor when not under power (safety measure).

Your circuit is overly complicated, but in essence to power a led from mains input you need to drop most of the voltage on something that acts like a resistor but does not get hot.