We recently had a subcontractor who's bank allowed them to cash a joint check without the supplier. If we have a joint check agreement in the future, is it legal to send payment directly to the supplier/vendor and not the subcontractor?
Generally, all payees must endorse a joint check for it to be cashed or deposited. In practice, however, it's somewhat common for a bank to screw that up. Sometimes, a bank will deposit a check despite the fact that one or more payees haven't endorsed it, creating quite the headache for the other payees.
As for whether a GC can directly pay a supplier, it's possible that the contract between a sub and a GC would allow the GC to "leapfrog" the sub and directly pay that sub's supplier. But, if the right to directly pay a supplier isn't explicitly reserved in the contract, a GC shouldn't directly pay the supplier. Instead, payment should typically be made to the subcontractor, who will then pay their supplier.
In the case of a joint check, the joint check should likely be paid to the subcontractor who will endorse the joint check, then make arrangements for it to be endorsed by the supplier and ultimately deposited at the bank. To make sure this happens, it might be possible to add terms to the joint check agreement whereby it's explicitly stated that the GC must provide the joint check to its subcontractor, who will then coordinate with the supplier.