Equivalencies of Powers/Rights is a good thought experiment that would keep the powers of the enforcers from multiplying without limits.
and if magnetic shit falls off my car, that's the breaks, suckers.
We were also taught it's almost never worth doing this; basically, if someone's shooting people and you're doing an armed job, yes, use your gun to try and stop them or detain them, but if it's just property damage or theft, call the cops and let them do their thing. The risk to you isn't worth it, nor is the risk of a false arrest lawsuit.
Then the question is, is such a good idea?
There was a curious case a few years back of a non-citizen who had been a military police officer and became a civilian cop because nobody checked his documentation. His military activities were perfectly legal but all arrests made as a civilian were invalid.
If a regular citizen can't plant a bug, neither can police. If police can conduct a stakeout, so can regular citizens. They just have to follow the same process. That might include going in front of a judge and getting a warrant.
If a regular citizen could break up a bar fight, the police should be able to take the same actions. If police can set up a sting operation, so should citizens be allowed.
Obviously, we don't want everybody running around conducting sting operations or traffic stops. So we set some bar for regular citizens that makes it less likely. But police should have to face the exact same bar. The difference is that we pay for their time, training, equipment, etc. If a certain level of training is required before anybody can make a traffic stop, that training should be open for anybody. We just pay the admission and the salary for police to take the training. Regular citizens foot their own bill.
Edit: poor proofreading