The Sandwich Islands that are mentioned often are the Hawaiian Islands. This was the name given to them by James Cook in 1778.
This is the only episode of the series in which the events occur entirely within Paladin's abode, the Hotel Carlton. Much of the action takes place in Paladin's hotel room (#314).
Since Colorado was the 38th state, admitted in 1876, and one of the Dakotas was the 39th state admitted in 1889, this episode takes place between the two dates. However, the Sandwich Islands (Hawaiian Islands) were not annexed until 1898.
When Romanov (Henry Corden) is sneaking into Paladin's room, a brief snippet of Tchaikovsky's 1812 Overture can be heard. Romanov then sings the same tune as he leaves the room.