The vacuum port is just open? That's an issue... and will certainly foul up the idle mixture. From what you describe, I understand it's the port on the outboard side of the intake manifold, below the carb? That port should have a rubber tube that routes to the vacuum wipers, if the truck has them, or simply have a rubber cap closing off the port, if no vacuum wipers.
To see if that's at least part of the issue, close off the vacuum port (you will probably need to adjust the idle speed screw to keep the engine running), and double check the ignition timing. If you have an issue keeping the engine running, check the adjustment of the idle mixture screw by gently closing it (not too tight, so that you don't damage the needle) and back the screw out to its nominal setting, which should be about 1-3/4 turns out from the closed position. It is certainly possible that it was misadjusted to compensate for the vacuum leak at the open port. If so far, so good, run the engine until hot, adjust the carb idle mixture screw for best idle at about 500 rpm, and readjust the idle speed if needed.
The misfire that occurs on acceleration captured on the video and the fact that at higher RPM, the engine seems to run fairly steadily suggests the vacuum advance on the distributor may not be working correctly. If the vacuum advance mechanism is working, you should see it rotate the distributor slightly when you open the throttle from idle.
Still having issues? I suggest pulling the valve cover, inspecting the pushrods and rockers, and adjusting the valves to spec as a next step. Initial setting of the valves can be done cold (add at least 0.002" to Intake spec and 0.003" to Exhaust spec), but final setting to spec is done with the engine fully
hot (intake 0.008" and exhaust 0.015").
BTW, if you haven't found the "vehicle information kits" on the GM Heritage website, they have a wealth of information on the original configurations of these vehicles. Here's the link for the '51 Chevy trucks: '51 Chevy Truck
. Engine information starts on page 135.
Hope this helps!