When O'Farrell says they have to follow the Southern Cross to the beer, the shot of the night sky does not show this constellation at all.
As is typical of Hope's period comedies, there are many anachronistic gags in the film; e.g. references to television re-runs, a reference to Burt Lancaster in 'From Here to Eternity', the hairstyles of the women and the bathing suit worn by Gina Lollobrigida.