The historic airliner used at the end of the film is a De Havilland Dragon Rapide biplane, built in Britain in the 1930s. This one is registration D-ILIT, and is privately owned in Germany. It is fully airworthy (as can be seen in the film) and appears at air displays etc.
Joseph Fiennes was originally offered the role of Lord Darlington, but turned it down to play Bassanio in Michael Radford's adaptation of The Merchant of Venice (2004).
The instrument being played in the band at the party is not a cornet, but a flugelhorn. In some of the musical selections, the sound heard is that of an unmuted trumpet, in others, it is that of a trumpet with a Harmon mute. The flugelhorn, as shown has an entirely different timbre.
In a brief shot before an evening party, what is presumably intended as a sunset is shown, with the coast on the left and the water on the right. In Amalfi this is only possible facing East.
When Meg finds the check stubs for checks written to Mrs. Erlynne, all of the check stubs have the same check number on them. They should be sequential.