Open-ended contracts are almost a guarantee that the final costs are going to be higher than you expect them to be. It is a way that added fees are inserted at the end of the job and final billing is made. The contract that you sign needs to have all potential costs spelled out so that there are no surprises in the final billing. Discuss with the roofer the additional costs for hidden damage discoveries and request that you be made aware of the damages as well as the costs at the time they are uncovered and not after materials have been removed and areas covered over. This helps to insure that no one is taken advantage of and you have the opportunity to agree with what will become added fees.
Though it is difficult to be exact about the damages that cannot be seen clearly, this is most likely not the first roof your roofer has installed. He is well versed in the matter of uncovering and making repairs to possible damaged areas on your roof. He is able to determine all costs necessary to make the proper repairs. If he is hesitant to offer a "not to exceed" figure for any unforeseen damage, request he spend a little more time surveying the roof, investigating the likely areas of concern and even a thorough check of the roof structure from the attic. We are sure that he will confirm the expected fees with you after this if he is a professional.
A good roofer will be glad to honor your request to witness all damaged areas on your roof and the method of repairs they intend to use.
This is an opportunity for your roofer to exhibit his skills, thoroughness and continue to build on a trusting business relationship.
If any additional costs and fees that are added to your bill without reference to the possibility of them in your contract, or without full discussion with you at the time they decide additional costs and fees are warranted, you should refuse to pay them. Good professional roofers do not operate in this manner and you don't deserve to be treated like this. Additional costs and fees are a way to make up for mistakes in the initial bidding or even a way to "low bid" your project in an effort to be awarded the contract and make up for the shortages at the end of the job.