what are the consequences/risks of writing a future date on a
document?
In the context of the OP this is harmless.
Indeed, the person signing them can probably revoke those signatures prior to closing on the date shown on the documents, if something comes up in the meantime.
I'd prefer answers that discuss the question more generally though.
The most common time this comes up is when a check is presented to someone as payment with a date after it is written. In that situation there are potential risks.
The intent when this is done is usually to prevent the check from being drawn upon until the date of the check, with the date of the check often being someone's payday. When this is done in this way, it is often called "payday lending."
The main risk in that scenario is that the person receiving the check will, intentionally or just accidentally, deposit the check before the date on the check, when there are insufficient funds in the check writer's checking account to pay for the check. This leaves the person to whom the check was written unpaid (although they can resubmit the check again to the bank after the first not sufficient funds rejection) and will typically cause the check account holder to incur a bounced check fee.
Generally speaking, the bank is not legally required to confirm that the date shown on the check has actually arrived when it is deposited, so this requires that the person writing the check trust the person to whom it is given to delay depositing it.
