First, I'd establish a relationship with the inspectors. They are wary and a little stand-offish because of frequent friction with landlords, but I've found that it's worth the effort to establish a trusting relationship.
Make sure you are present (and very pleasant) when the inspections are done. Take copious notes while you follow the inspector around. Maybe have you handyman present and start on the easy fixup items even before the inspector has left.
Why go to this trouble? A relationship with the inspectors won't mean they will overlook a major issue, but they may let you slide on some minor issues. It's also more likely that you can pull a favor and the re-inspection will get scheduled first = your tenant can move in earlier.
After the inspectors, try to develop relationships with the individual case-workers. Always refer to their "clients".
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