Yesterday I arrived at the office 3 minutes late. I apologised but got a verbal warning. This is harrassment, or I am over-reacting?

If it was a simple verbal warning, that isn't harrassment. When the boss mentions it 3 more times in the day, thats harrassment. He has a right to warn you.

Most places I have worked - you can be "late" a certain amount of times a month without consequence --- either in the morning or back from lunch. After that --- there should be a system in place of how to deal with things to be fair.

I wouldn't call it harassment, but whoever said something to you definitely has a stick up their ass. Three minutes is close enough it's not even late. That's a small enough difference it could just be the difference between your watch and his.