Can a zoning enforcement officer enter your property?

Disclaimer: I am not a lawyer and am only presenting the facts as I understand them to be true. I may or may not be correct in my interpretation of the law. This is not legal advice. Please be advised that the court's interpretation of the law in your jurisdiction may or may not be congruent with my statements.

This will depend upon the reason and circumstance surrounding said trespass. This will also depend upon your local jurisdiction. Most lawyers will answer these questions through email if you simply write them. But be very descriptive. If you do not present time, who was present, reason for trespass, etc you will not get an appropriate response. Pick a lawyer in your area who specializes in civil liberties. Here is a good place to look.

ACLU lawyers are notorious for providing Pro Bono (free as in beer) services to those who need them or deserve them. All state bars will require lawyers to do a certain amount of Pro Bono time in a certain time interval. Many times this is how we receive our gracious public defenders.
It depends on few factors. One, was it an emergency? Two, were the owners of the property notified with the exact date and time of the inspection and for what purpose? Three, were there signs posted such as "Private Property, No Trespassing" on the property? Was there court order issued by the judicial powers in the area.
Municipalities are subjected to the same and perhaps more stringent scruples when it comes to land laws. City employees found violating these laws are subject to criminal investigation and charges. Further, if the city employees broke the law as a result of a direct order from the manager or council, criminal charges can be brought against the municipality naming the heads of the departments, the council members and the mayor. Municipalities usually have a lawyer to consult with these issues. It wouldn't be however, the first time the municipality got their wings clipped in court.