In Visconti's film you can see the royal italian flag. But wasn't Venice at the time of Mann's novella a part of the Austrian-Hungarian Empire? And also the scene where Aschenbach is in the bank: Was at that time already the Lira the currency in Venice?
Although parts of the Veneto and the Venezia Giulia (Italia Irredenta, giving rise to the term irredentism) remained part of the Austro-Hungarian Empire until 1918, the city of Venice itself became part of the Kingdom of Italy at the end of the Seven Weeks' War, in 1866.
If the Kingdom of Heaven is like a grain of mustard, It can also be like a chicken-pox mark.
In movies, they frequently used to overlook hair when it came to period authenticity. Lots of World War 2 movies, for example, have people sporting hair of a later decade. Medieval movies in the 1950s frequently had knights with Elvis-like hairdos.
Visconti is famous for being one of the most fastidiously perfectionist directors of all time. I don't think he would have overlooked details such as flags, hairstyles, etc.