I see your point, Astro, though I would have been really upset at being accosted in my own home, too. IMO, the officer should have apologized for the mistaken charge and disengaged, even if the professor was "ranting and raving", instead of escalating the situation to an arrest, charge, and booking. After all, how many burglars are 58-59 years old and plying their trade in broad daylight in a nice neighborhood? Yeah, Crowley was probably embarrassed by getting dressed down, but that's no reason to arrest the professor. The officer's escalation of the situation (vs disengagement) was immature, IMO. I do not hold Gates blameless if he indeed verbally abused the officers, but the offense should be tempered by the context. He had returned from a trip abroad and was sick (and probably tired), and was unable to get into his house. Then he gets rousted by some Cambridge cops for trying to get into his own house.
I don't think that Obama owes the police union an apology because he's right. The situation should have been resolved quietly, and the arrest, booking, mug shots, etc, amounted to an insult on the professor that was unwarranted, given the circumstances. He was just trying to get into his own house, after all. I have quite a number of close friends and relatives who are in law enforcement. Given the very rural nature of this state and the paucity of back-up, the troopers, wardens, and sheriffs here are pretty darned diplomatic on the whole.
Here's an example: My friend and musical partner called one Sunday morning to tell me that he had been picked up for operating under the influence and that he would be losing his licence, which would put a stop to our ability to perform as a duo all over the state. He was pretty distraught, so I drove up to his place to keep him company for a bit, and the arresting officer (a state trooper) stopped in at his apartment to see how he was doing. The trooper lived in town, and wanted to make sure that Tim was OK. The trooper retired from the state police and ran for county sheriff. One of the best sheriffs we have ever had. These officers work alone - they are tough as they need to be, and as reasonable and diplomatic as they need to be.