Point at

[ROBINDESBOIS]

Difference between point at/to/out?

[Rusty]

They can all mean señalar (con el dedo), but in context they can also mean apuntar, mostrar, tocar, dar a entender, dar a saber, llamar la atención, destacar and afirmar (there are most likely other meanings).

Tough question.

Point at/to/out the Big Dipper.
(If both parties are gazing at the night sky, the different usages can only mean 'use your finger to show me where in the sky I can find the constellation'.)
(If a map is being examined, each command could mean 'point your finger towards the area on the map where the constellation is located'.)
(If I point my finger towards the area, but you're not certain which stars I pointed at, you could repeat the command, or use another one of the prepositions, to mean, 'This time, touch the map'.)

I'd like to point out that we won the last game. ('Point at' or 'point to' cannot be used in this instance.)

All our efforts point to a successful game. ('Point at' or 'point out' cannot be used here.) ('Point toward(s)' could be substituted.)

[ROBINDESBOIS]

All Greek to me !

[Awaken]

I think it is just a case by case thing. This is definitely getting into gray areas where sometimes 2 of the 3 work fine, but one is more common. To/At can be used interchangeably most of the time, but Out seems to be used a little more uniquely.

It seems more common when you don't want to be identified that the term "at" is use. "I'm not doing that! The boss pointed at you" or "He pointed at the defendant."

Pointed out usually goes along with "to make aware of". "He pointed out my mistake" or "He pointed out that we only won the game on a bad call by the umpire"

When something is within reach/touching distance, pointed to seems to be the most common. Point to it on the map.

A lot of the other stuff is gray with the use of "at" vs. "to" so don't worry too much over it.