What separates a plainclothes cop from a crazy road-rage person in your rearview mirror?

I had a confusing WTF incident while driving to work this morning and would appreciate your constructive feedback and advice.

I was driving from Storrow Drive towards Kenmore Square with the goal of getting on Beacon St. to end up in Brookline. Map here:

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I made a right turn from the right-hand lane from Charlesgate onto Beacon St. If you drive through this intersection regularly, you may know that this section of Beacon is one-way and has two lanes. As you approach Raleigh St. and Kenmore Square, a third lane opens up on the left that is typically flanked by parked cars. I usually pull into this lane to go straight through the light at Kenmore to continue traveling on Beacon. As the lane opened up, I looked to my left to make sure no cars were approaching and seeing none, I turned my vehicle to the left and proceed to drive into the lane.

At this point a car starts honking. I look again to my left and there is a brown/gray sedan suddenly in the lane I am turning into. I assume I am the jerk here and have possibly cut someone off that I didn't see and the male driver is yelling at me. I mouth the words "I'm sorry" but the man is really upset and still honking. I start to get nervous that I've got a road rage person on my hands. Suddenly he starts flashing a blue light from the inside of the car and I think oh no, is this a plainclothes police officer in an unmarked car?

I pull over not 100% sure this was a cop - isn't one supposed to ask for a badge or call 911 to verify someone is indeed a police officer? - but didn't want to take any chances either. I pull over to the side of the road near Bertucci's and he pulls up in his car next to me. He is not wearing a uniform and did not produce a badge, but I was pretty freaked out by him at this point and did not ask to see one. He yells that I failed to yield to him while driving and threatens to write me a ticket. I apologized again and again and stated that I didn't see him in the lane I was moving into. He never got out of the car and drove off. I felt confused and somewhat frightened.

Some questions:
- What are BPD policies regarding plainclothes police officers in an unmarked car? I've looked here but was unable to find information:
http://www.cityofboston.gov/police/rules.asp

- Can one be mailed a traffic ticket?

- What would you have done? Any tips for driving through this intersection better next time?