My large company customer has its own form contract for my services. I don’t have any bargaining power with this customer, so why should I have the contract reviewed?

You would be surprised at how reasonable most large companies can be when it comes to negotiating contracts.  Yes, you generally have to deal with their legal department rather than the contact you have within the company, but the legal department is used to negotiating contracts.  That said, it’s true there will be large portions of the contract that are non-negotiable if you want their business.  Those provisions really need to be reviewed by legal counsel so that they can be understood by you so that you do not inadvertently breech the contract.  Under no circumstances should you agree to a provision that you cannot possibly fulfill (staffing comes to mind; so does insurance).  If you lose the contract because of that, so be it.  Better to lose the contract than perform the work and later have the large company refuse to pay, in whole or in part, because of some unfulfilled provision.  And beware of audit provisions!  Understand that if there is an audit right in the contract, you will be audited.