Where do you draw the line to crimes that you witness? Are there some things that you don't particularly care about that others might report, like observing a drug deal? Maybe you have a story to tell about something you witnessed and let slide?
I'm an American living in Mexico. I don't expect the police to be of much help. In fact, if one invites the police into his home for any reason, he is likely be robbed. And I expect the policeman to take the side of any Mexican over ant foreigner.
Furthermore, if the crime reported is cartel related in any way, it could be dangerous to report it. So, we don't go to the police for anything.
The way we've adapted is with local Facebook groups, including crime watch sites, where people let one another know what to be careful of. Purses are frequently stolen in Wal-Mart or a parking lot. Sometimes the ruse begins with mustard or ketchup squirted on the victim as a distraction. Nobody will call the police if victimized by this. They'll just discuss MOs and security measures among themselves on the Internet such as purses with straps that can't be cut, security belts, etc..
I haven't interacted with a local police officer since about 2012, when it was a traffic stop, which brings up another interesting wrinkle for people used to living where police corruption is the exception rather than the rule. Our local police are paid so poorly that they routinely try to get foreigners to pay a bribe rather than a ticket. The bribes are cheap (I've paid $10 USD once and $25 USD once, in pesos of course), and easier than going down to the municipal office to pay a ticket, but they are illegal to request and, as I've recently learned from these Facebook groups, illegal to pay, but it is almost impossible to be caught (they expect you to put the money down in the car with door open so that nobody sees you or the cop with the money).
But when living in the states, I wouldn't hesitate to get the police involved if help were needed.
But to answer your question, did I report all infractions that I witnessed in the States? No, at least not to the police. Many, but not all. I would probably inform the victim in every case possible. I didn't report an office employee that tried to steal second paycheck for a pay period. I just fired her.