I'm actually a programmer, but I happen to have a cubicle right next to the claims adjusters, and I am able to hear both sides of the conversations clearly, and I often have conversations with the adjusters about common mistakes that people make. Here are a few things that come up very frequently.
1) Know what your policy does and does not cover. Don't blindly sign an insurance agreement until you have read the entire document at least twice, and asked for clarification when you don't understand a clause. Some of the differences between coverage and no coverage seem quite arbitrary, but they are important. For example, you may have what's called a 'contents-only policy'. This means that if a pipe bursts inside a wall, and floods your house or place of business, the company is only obligated to pay for damaged contents (carpets, furniture etc.) You will be responsible for repairing the pipe and the wall if it was damaged. Flooding is another good example. Many companies make a distinction between water seeping in from the outside of your dwelling, and water coming from the inside. If an inside pipe bursts, you will probably be covered. But if the municipal sewer backs up and floods your dwelling, you may very well be SOL. Make sure you ask your agent to outline all the possible scenarios.
2) In many cases, you will have to make emergency repairs in the middle of the night and will not have time to notify your insurance company, let alone wait for an independent adjuster to pay you a visit. If that is the case, take photographs and video of the damage before effecting repairs. The more the better. And keep all receipts from emergency contractors if you do hire one to repair the problem. And hang on to all damaged equipment that has been replaced. If all you have to show the adjuster is a repair that you did yourself, your claim will almost certainly be denied.
3) Following from the above, you have a duty to prevent further damage to your property. If your carpets are flooded, turn off the water to your house immediately, and then hire a reputable company to dry out the premises ASAP. Tell them that you will be filing an insurance claim, and they will document the damage before starting the drying process. If you wait a month before calling your insurance company, and your baseboards are now rotted and mold is growing rampant everywhere, don't be surprised if your claim is denied for 'failure to mitigate'.
4) If you live in a community governed by an HOA, or are leasing a dwelling from someone else, make sure that you give your agent a copy of the HOA Deeds and Covenants and/or your lease agreement. Most of the time, these documents will spell out who is responsible for payment should something go wrong. These documents supersede any clauses in your insurance policy.
5) The age of 'slip and fall' and 'I burned myself on your soup' are long past. Juries today have become far more skeptical. Two cases that stand out (I also talk to the legal team quite frequently) - a woman sued a well known take-out restaurant for burns sustained when she handed a closed cup of hot soup to her daughter in the back seat of her car and dropped it, spilling hot soup all over her daughter's legs. She sued for two million dollars. The company offered her $100K as a settlement. She declined and the case went to court. The jury deliberated for less than two hours, and the found for the defendants. So not only did the plaintiff pass up the chance to get $100K, she ended up with nothing but a large legal bill. A similar case was a familiar 'slip-and-fall'. The plaintiff wanted $250K for injuries. The company offered $10K. In court, the defendants showed the jury security camera footage of the woman walking right past a 'Danger - Wet Surface' sign and the employee that was in the process of mopping up the spill. The jury found for the plaintiff - and awarded her $500.
In short, insurance can be a good thing - if you know exactly what it is that you are paying for. It's far too late to argue with an adjuster after the damage has already been done.