Private Investigators aren't allowed to trespass on other people's home to recover information & aren't exempt from trespassing legislation unless serving legal documents. We need permission from the owners in order to search a property.
While certain disguises are acceptable and can be utilized effectively, Private investigators aren't permitted to pose as law enforcement officers.
Private investigators are not given any special powers of arrest beyond what a normal citizen is permitted. We regularly use surveillance to discover details regarding criminal activity but as guided by our clients, usually we wouldn't get involved and turn the information over to law enforcement, working with the best criminal lawyer in the region, usually. Private Investigators are allowed to carry weapons either openly or hidden as long as they've received licenses to take from the correct government service.
A professional personal investigators do and can access social security & license plate numbers; however, these private pieces of data are strictly controlled and can't be accessed without a permissible purpose. A permissible purpose will incorporate something like needing to locate a person to serve them or confirm that a particular vehicle is registered to a suspect, but NOT to try to find a celebrity or spy a neighbor because you don't like the color of their hair.