The law you are referring to was originally called the The Law Enforcement Officer's Safety Act. The law is sometimes called HR 218 and the official title of the law, due to a recent change, is called The Law Enforcement Officer's Safety Improvement Act.
The law is codified under Title 18, Part I, Chapter 44, Section 926b, "CARRYING OF CONCEALED FIREARMS BY QUALIFIED LAW ENFORCEMENT OFFICERS"
The law, in short, allows any law enforcement officer to carry concealed handguns if they have statutory powers of arrest, qualify by their department standards, are not under disciplinary actions, not prohibited from federal law, and are not under the influence of alcohol or hallucinatory drugs or substances. The law enforcement officer must carry their credentials on them while carry a concealed handgun.
There are exceptions to where an law enforcement officer can carry. The places that you cannot carry are in state or local government facilities that restrict carrying (schools, state, city or county offices, and so on), court houses, and private property prohibiting carrying.
With the recent passing of The Law Enforcement Officer Safety Improvement Act law enforcement officers are allowed to carry ammunition that is not expressly restricted by Federal law or the National Firearms Act. So to the best of my knowledge, if there is a state or locality that prohibits Jacket Hollow Point bullets, then the law enforcement officer is exempted from that law.
With the above being said, technically in the State of Oregon a off-duty law enforcement officer could not carry a concealed handgun onto school property unless the law enforcement officer had a concealed handgun license or was on official duty because the way the federal and state law is written. Also, in Oregon there is no specific law prohibiting a person from carrying a concealed handgun while under the influence of alcohol. So in that respect, there are greater restrictions placed on a law enforcement officer.
In regards to being a law enforcement officer twenty-four-seven, that is department specific per policy. In my department, we are not required to carry our department firearm nor qualify on our off-duty handgun. Our policy is very specific about us being a regular citizen, only taking action we are personally responsible for, and not producing our credentials unless it's for verifying our employment.