If you don't let the inspector in the first time, there is the chance that upon return the inspection will be much more thorough and comprehensive because of a belief that you were trying to hide something. If you don't make them get a search warrant, then inspectors can look anywhere you allow them to look. If they have a search warrant, then the warrant will describe the extent of the inspection. Inspectors can take photos and measurements, and test air and water samples. They can also speak to employees privately if they want to and if employees consent.
Most inspections are the result of employee complaints.
The second-leading cause of inspections is workplace injuries. If you think the inspector is wrong, then you file a notice of appeal with the Appeals Board. You will then have a hearing before an administrative law judge. There are no juries for these cases. The hearing is more like an arbitration that uses relaxed rules of evidence.