While it may not seem fair, there are immunities in the Califoria Government Code for negligent inspections. Therefore, the City would not be liable. The property owner's recourse would be against the contractor. The policy reason is that ciities are not guarantors of the contractors work.
Ultimately, the property owner is responsible for making sure his property is accessible. Sometimes the responsibility can be passed on to a tenant. In your case, the contractor might have some liability.
The City, however, would not be, even if the inspector did not catch everything.
When ADA lawsuits are filed, they typically name the building owner and any tenant.