I have been unfortunate enough to deal with insurance companies on some major issues several times in my life. The 1st thing like others said is to document everything, not only your possessions, but every phone call that you have with their adjusters, claims people or whoever. Find a good contractor to do the repairs/rebuild. If you find a good contractor they will go to bat for you. They want to make money too and they will send in estimates, they will tell adjusters things they missed and they will make sure you are taken care of. If all else fails hire/threaten to hire a lawyer. I am sure this is different in all states, but in Michigan this is the last thing they want. It looks bad on their business and they lose more often then not from what a friend has told me in that is in the insurance business.
My personal story, about 4 years ago we had a major hail storm hit our town. When I say major I mean this hail was the almost the size of a baseball. We got our truck coverage by insurance with no problem. Our house however was a huge problem, they replaced the entire roof with no questions asked, but when it came to the siding and windows, and screens we had a major problem. It was aluminum siding and because the storm had mostly hit the north and west side of the house they only wanted to cover that part of the house. Anyone that knows siding will tell you that you can't match up aluminum siding, your house will look like it is 2 different colors, plus the winds were 50+ mph hour and it ripped siding off the east and south side. At first they tried to claim that because we were going to go with vinyl siding to replace the aluminum and aluminum was more expensive that only covering half the house would pay for the entire house to be resided, but our contractor called them out on that. They then tried to claim that the siding should have been replaced before this storm and thus they weren't liable for those damages. So basically the wind blowing off the siding was our fault. So we contacted a family friend (a lawyer) and he sent them a fax. I have no idea what it actually said or threatened, all I know is someone from the corporate office contacted us the next day and said everything would be taken care off and that our entire deductible was waved.