When building our house, we didn't go with a third party inspector but we were pretty involved with the building process (ie. met with the architect, met the owners of the company and knew at least one member of every process - framer, electrician, etc.).
The city inspection is really poor IIRC. I don't think they really looked at the pipes and other things they really had to use some effort seek out...I distinctly remember them looking over the appliances really well, though.
With a larger builder like Albi, I think you will be okay.