Common pitfalls in landlord insurance policies

Hello fellow investors,

I'm a beginner investor looking to purchase my first rental property. However, I read Brandon Turner's book "The book on rental property investing" and the section on lawsuits got me a bit nervous. While I'm working to find an insurance broker to help me find a bullet proof insurance policy when the time comes, I also wanted to get advise from other experienced investors about getting insurance as a landlord. Below are the questions I'm seeking answers to:

1) Are there certain types of cases that most policies don't cover but lawsuits  related to them are fairly common?

2) Are there any circumstances in which tenants cannot sue the landlord?

3) Would it be advisable to include a clause in the renters agreement stating the landlord will not be liable in case of injury caused by tenant negligence? 

Any suggestions on common pitfalls or books containing detailed information on insurance is also much appreciated. 

Thanks,

Rishit