Air Carrier Captain reported being notified at destination that an incorrect Dangerous Goods Form was delivered at departure and accepted by Captain.

Narrative

When presented with the Dangerous Goods Form; I noted the correct flight number and departure and arrival gateways; but failed to notice the incorrect tail number and flight date. I received a notification to contact my dispatcher after arriving at RFD. When I did so; my Dispatcher informed me that I was given the wrong Dangerous Goods Form for the flight.ZZZ HAZMAT Office Personnel provided me with a copy of the Dangerous Goods Form I signed and informed me that the Load Supervisor had both the correct Dangerous Goods Form in his hands along with the incorrect Dangerous Goods Form given to me. The Load Supervisor inadvertently handed me the incorrect Dangerous Goods Form (same flight; different tail number from a previous date) and I failed to notice the discrepancies.Aside from better diligence on my part; I have two suggestions for prevention of a future similar event.First; load planning should be restricted from transmitting to the load docks Dangerous Goods Forms from previous flights and dates.Second; A-300 AOM procedure should be changed to assigning the primary duty of closing the cargo door to the First Officer rather than the Captain.The last few minutes of cockpit prep (Dangerous Goods Form review and completion of the [departure] process) are very busy for the Captain and mostly idle time for the First Officer. Most times; the First Officer can be closing the cargo door while the Captain is in the process of reviewing the Dangerous Goods Form and completing the [departure] process. This change would relieve some of the time pressure often experienced by the crew and help in avoiding mistakes.If I remember correctly; First Officers were assigned the duty of closing the cargo door for a number of years after we first started operating the A-300. The AOM does allow for First Officers to close the cargo door; but it might be better to standardize that as a primary duty of the First Officer. It would have the additional benefit of savings precious time.I will consciously slow my final cockpit prep to avoid repeating this oversight by more closely focusing on the information I am supposed to review.