If a roofing co that did a poor job on my roof, do I have to pay them?

You typically only have to pay for work which is done to generally acceptable commercial specifications or standards--which is not the same as saying it has to be "good" work, just "good enough," which is lower standard. And even when the work is not fully up to specs or standards, you typically have to pay a portion: for example, if the job was $10k, and because it was not done fully properly, it will require $3k to set it right, you would typically have to pay $7k, offsetting the other $3k against the cost to correct.

One way to handle this situation is, if they are unwilling to correct the deficiencies, to get some estimate or proposal for the cost to correct (e.g. from a home inspector); then offer to pay them what you owe less the cost to correct. If they agree to it, get their agreement in writing; if they don't agree and you don't mind taking the chance of being sued, pay them the appropriate portion, together with a letter spelling out the findings of the report and why you are not paying in full. If they should sue you or take other action for the rest of the money, you would defend on the basis of their unacceptable work and the estimate as to the costs to correct and, in the meantime, have established good faith by paying what your inspector documented as the correct or fair amount.