OK this is easy. The answer is NO.
The construction has issues:
- There are no bolts for the sill plates.
2.The sill plates should be spaced on the slab so that wall plus exterior finish meets slab. It looks like this house is getting brick or thick stone given the 3 inches or so from the edge.
I am not sure about your situation. You are having a house built. If it were me I would not pay this person another dime. He should know this stuff if he is building a house. He shouldn't be unsure of this. If he is putting concrete nails in this (which I think is only code if you live in a shed) then what else is he doing?
To fix this situation everything needs to be ripped out. He is going to have to use a hammer drill to drill down into the slab to install anchors. The holes for the anchors need to be on center of your framing. I am not sure your builder could handle this. Also drilling down anchors is really a half-ass way of doing this (in my opinion). These are not as strong as anchors poured in and tend to wiggle.
Get your building inspector out not a 3rd party that could be as bad as your builder. I would also ask the inspector for local code regarding anchoring post-pour. I would personally look into my builders credentials. If I continued using the builder I would make sure the city understands your lack of confidence and that they should be looking at everything closely.