Inspections
Inspections of business, residences, and other private property is a core public health activity.  Whether looking for standing water that breeds mosquitoes or for improperly maintained buildings that harbor rats, public health inspectors have broad powers to enter property to address public health threats.
Inspections are legally classified as an adjudication.  The inspector is the judge and investigator.  The party being inspected may accompany the inspector and present his side of the case during the inspection.  The party is given a written report outlining problems and may appeal an adverse determination, such as a restaurant closing, to an administrative body or the courts.
License and permit holders agree to allow inspections during business hours or other appropriate times as a condition of continued operation.  If a licensed business refuses an inspection, it can be shut down pending compliance. 
Health departments often conduct public health inspections of private residences and businesses that do not have health department permits.  These may be fire inspections, rat inspections, or other general health and safety inspections.  While these inspections were traditionally done without a warrant,[Frank v. Maryland, 359 U.S. 360 (1959)] the United States Supreme Court now requires a general or area warrant if the owner objects to the inspection.[See v. Seattle, 387 U.S. 541, 18 L. Ed. 2d 943, 87 S. Ct. 1737 (1967) and Camara V. Municipal Court City And County, 387 U.S. 523, 87 S. Ct. 1727, 18 L. Ed. 2d 930 (1967),  Generally, Searches] These warrants do not require probable cause or specific information, but are based on general criteria such as periodic inspection timetables.  If an inspector is refused entry, the usual procedure is to seek a court order requiring compliance with the inspection.  If the owner does not comply with the court order, the court can impose contempt sanctions.
Administrative warrants cannot be used as a substitute for a criminal due process warrant. This is an important issue in joint public health/law enforcement investigations. The courts have carved out certain exceptions for closely regulated business that allows prosecution for information gained through administrative searches, but these exceptions are limited.[New York v. Burger, 482 U.S. 691 (1987)]