I've been in a newly built house for just less than a year and have two items that I'm concerned with. First, the some of the motar separating the bricks on the first step has degraded to a point to where there are air gaps of ~1/4 to 1/2" between bricks (e.g. motar has completely disintegrated in some places). In other places the motar is cracked and is only a matter of time that it completely fails. I'm going to have the builder come back out to repair, but I'm seeing some indication of motar failure in other locations on the steps that may indicate that given enough time, other areas of the entry steps will also weaken. QUESTION: My plan is to have the builder come out and make repairs to the observable damage, but how much concern should I have with the rest of the step structure?

Second, on the same set of steps, I noticed in a gentle rain that water pooled on the 3rd step. We live in a fairly moderate climate (South Carolina), but at times the temperature gets below freezing and this could ice over. QUESTION: Is there a building code that requires steps to not accumulate water? (This seems like a no brainer, but I have to ask.)

Steps should not be holding water, it is is pooled it means it is not level or properly slooped.

I would pay for a good home inspection to find other problems that may be hidden or unknown to you.
Then go back to the builder, (if of course there was a warranty sold with the home or depending on the contract you had with the builder)