What are the pros and cons of shifting a car constantly into neutral?

It will only add slight wear to the shifting mechanism. But you should be holding the brakes on anyway, for three reasons:
-whenever you are stopped in traffic, you should have your brake lights illuminated;
-the car may begin to roll, without you noticing it;
-should your car be struck by another, it will move less, possibly avoiding a collision with more vehicles (or pedestrians!).

Any fuel savings would be minimal: At idle, your fuel consumption is extremely low either way. You can save FAR more gas by driving conservatively: Lower your speed on highways, and avoid hard acceleration. Also, maintain correct tire pressures, keep the car in good tune and don’t carry extra junk in the trunk.

You are gaining nothing. As far as the brakes the car isn’t moving so you aren’t putting any wear on them. It’s just a bad habit your getting yourself into.

as far as the transmission, no. the only thing is you are using your clutch more,therefore premature clutch wear,don’t worry to much about it,almost every one does this. I am not talking about wearing it out quickly,I am talking about in the long run.

Drivers with manual transmissions can’t let the clutch pedal out in gear until they’re ready to accelerate or they’ll stall the engine. So they may shift into neutral during a long traffic stop like you do with your automatic transmission. You can both turn the engine off altogether when you have to sit in traffic a longer time.