Over the prison there is a 40 star flag (5 rows of 8), in the courtyard outside the prison there are 38 star flags.
When Young Jun and Father Jun look off in the distance and see a steamship waiting to take the Chinese back to China, the ship in question is about 25-odd years too early. At a guess, the show runners confused the 1870 Oceanic with the 1899 Oceanic. The former was doing cross-Pacific runs as of 1875, but had sails and sailing masts, was notably smaller, and looked much less like a classical "steamship" such as the Titanic.