Difficult to analyze without photos. You are probably referring to the screed board that he leveled off the top with--a board long enough to ride on top of the forms, then I guess he didn't steel trowel it. There is a chance that some of what you call pitting (which was probaly caused by air bubbles left unattended) could possibly be closed by rubbing the surface as discussed in this link, since the concrete is still "young".
The two inch gap was probably left where the bottom of the step face form (riser) met the surface of the new sidewalk due to his doing no finishing and it was an area the screed didn't reach well. If I am picturing this correctly (have to just guess) in order to avoid a safety problem of someone getting a toe in that gap, you would have to do some grinding of the face of the step to try and get a smooth line. If you can't get rid of that gap someone will eventually get a toe in it and fall flat on their nose. Hope you are curing it keeping it wet or the bagging to get rid of the voids probably won't work either.
Smoothy's approach is best I must admit and if you can afford it, starting over and doing it right with the right tools and people is definitely the right way to go. I'm betting that the mix was too wet and he was screeding water instead of concrete in the low spots. The window for even trying to fix the voids is very short (especially if it has been left dry). But if you can't fix that gap (trip point), forget about the bagging of the other surface. Good luck.
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