The most trouble I've ever gotten into for shooting (mainly, video) without a permit or insurance, was simply a request to stop shooting. Most municipalities can write you an infraction that carries a fine for about $500 (e.g., Beverly Hills), but these are rarely ever issued, and mostly apply to filmmaking, not stills. If you're shooting news or a documentary, all bets are off, and you have a lot more leeway to shoot without permits or insurance.
I also believe that, from my own observations, that since the development of low-cost 24p video cameras, and the rise in popularity in pro-level DSLRs used by hobbyists, much of the enforcement of these restrictions have been relaxed, simply because so many more people are shooting now. So, this is a trend that's going in our favor.
The US is generally fairly lenient on public picture-taking in my experience. Here's some general guidelines which apply throughout the state of California, and I assume, for other states in the US as well (with the exception of California's recently passed "paparazzi" law):
1. Photography on private property is typically not permitted without permission, a release, and typically, liability insurance for $1-2 million in coverage. This includes retail stores, shopping malls, business parks, etc. If shooting in a national retail store, permission may be requested from the corporate office's media relations person.
2. Photography within the Los Angeles Metro subway system appears to be generally tolerated, but not encouraged, and may sometimes be prohibited depending on the type of shooting (stills vs. filmmaking). No tripods are allowed on any train platforms.
3. Surprisingly, LAX has no specific restrictions on photography. TSA will prohibit you from shooting security areas. Airport police may question you, but I have been told by airport police that, "It's legal for you to take pictures here."
4. Generally speaking, if you're on a public sidewalk, you are legally allowed to take pictures of anything from that vantage point. However, you may not block a public walkway with equipment, or yourself. A police officer or fire official can make you move from the sidewalk if you're viewed to be causing an obstruction, or hazard to pedestrians. Unless you're inside a police or fire line (or, in some sort of other immediate danger), police officers typically may not prohibit you from shooting from any public sidewalk.
5. A few State of California "paprazzi" laws have been passed in recent years. These laws mainly address the use of ladders and extreme telephoto lenses when used to peer into private residences from a vantage point that would normally be unavailable at eye-level.
6. Museums vary from venue to venue. Some allow photography, some do not. Most do not allow the use of tripods. Virtually all do not allow electronic flash.
7. Theatrical venues vary as well. The Dorothy Chandler Pavillion does not allow cameras. I was able to bring a camera into the Disney concert hall to shoot the Los Angeles Philharmonic, but I don't know if this policy varies by performance or not.
A few caveats:
Note that if any fire department official (e.g., a fire marshall) tells you that you cannot shoot, he has the power to have you arrested if you don't comply with his instructions. Park rangers also have full police powers of arrest. Airport police are "real" police, and their jurisdiction extends to the city surrounding the airport. Any police officer (CHP, LAPD, etc.) from any California jurisdiction can arrest you, or issue you a ticket, even if you're not within their municipality or area of "official" jurisdiction.