Air carrier Captain reported the documentation for the transport of HAZMAT cargo had erroneous information that indicated the cargo was scheduled for a different flight and date that went unnoticed until the Captain reexamined the document later in the flight.

Narrative

Prior to pushback; the Operations Agent visited the flight deck and dropped off a Dangerous Goods Form for HAZMAT and new Releases that included the HAZMAT in the Dispatch remarks. I looked over the Dangerous Goods Form and it appeared correct; verified that HAZMAT was noted on the Release; signed both copies; and handed one to the Operations Agent. Later in the flight; I scrutinized the Dangerous Goods Form more carefully and realized that it had been created on Day 0 - today; but indicated the shipment was for [another] flight on [another] date. I contacted my Dispatcher via ACARS with the information and he phoned the ZZZ Station who assured him that all was correct and the HAZMAT was onboard the aircraft. Regardless; there was obviously a discrepancy; so when we parked in ZZZ1; I went down to the Ramp and observed that the HAZMAT was being unloaded and had in fact been on this flight and not tomorrow's. Given the elevated level of attention being given to our HAZMAT processes; I felt it necessary [to] highlight this discrepancy in the paperwork provided to the flight crew.A more thorough review of Dangerous Goods Form would have caught the error but really; expectation bias i.e.; the expectation that the Dangerous Goods Form would accurately reflect the date; played a role. Perhaps our Dangerous Goods Form workflow could incorporate some safeguards. It may be an unrealistic expectation for the Captain to trap all these errors moments before pushback.