Even allowing for the fact that it's a dream: Burr shoots Hamilton twice. Dueling pistols only held one cartridge.
The minuet played in the 1804 dream sequence was composed by Jan Paderewski in 1887.
Because the Hamilton story is in a dream, this could be attributed to real life being altered when it transfers to a dream: Ben Franklin is shown here, but the real Ben Franklin died in 1790.