Painting a pool with concrete showing through the plaster

I just bought a house with a pool and would like to get it ready for
summer. I drained it for painting and am now concerned about several
eight inch patches of concrete where the plaster is worn completely
away.

Can I get away with just painting over the concrete or do I need to
patch these areas? If I need to patch them, does anyone have any
pointers or links to pages with instructions? Does the pool need acid
washing if it's free of alge and other scumminess?

Also, I am not concerned with having a perfect looking pool and, since
we just bought the house and are a bit short on cash, I would like to
avoid any unnecessary expenses. However, I am interested in properly
maintaining is so that I minimize future problems.

Thanks in advance for any advice.