I would fill them with concrete too, but, that retaining wall is not high enough. Water is going to come down that hilly right above it, and gush right over the top of it. Is there a reason, the retaining wall is so short.

Why are the holes there?

Not knowing all the facts, I assume the holes are there to accommodate a railing that keeps people from falling over the edge of the retaining wall, they are there for safety purposes. Is there a hazard created by filling the holes and not having a railing at the edge of the drop off?

My home is the 2nd to the last home on a slope 1st picture is retaining wall on the left side of the house next to the last home on the street. This is the retaining wall the post holes are not covered up.

2nd picture is retaining wall on the right but the post holes are covered up. Im not sure why post holes on the right is covered up and not the left or not sure the purpose of the holes other then the obvious reasons the fence. Maybe the builder forgot to cover them. Should I be concerned for possible damages to the soil/foundation from the post holes being expose to water and debris. There are cracks on the mortor and the bricks. Previous picture #1 On the lower level of the retaining wall you can see lot of water after a rainstom, is this normal?

" Should I be concerned for possible damages to the soil/foundation from the post holes being expose to water and debris. "

Of course and I already answered that above, especially if you are in region that gets snow and freeze.

You will have water there, and no, thats not normal. The retaining wall, should be taller than the highest point of the yard, and there should be other drainage on that high side too, to drain the water to a ditch, or drain of some type. The wall is way lower than it should be, so it isnt doing much of anything.