While the main character, Peter Stuyvesant, was a real person and New Amsterdam was indeed a Dutch colony, don't consider "Knickerbocker Holiday" to be a history lesson. This is okay, as it's obvious that the musical comedy film isn't trying to be a historical piece and was based on a Broadway musical. Instead, just enjoy the story which was based very broadly on this colony.
The story is set in New Amsterdam in the 17th century. The town has been run by a group of repressive kleptocrats who are more concerned with bleeding the townsfolk of their money than anything else. When the new governor (Charles Coburn) arrives, folks are hopeful that he'll institute reforms...and at first it appears this will be the case. But Peter Stuyvesant is a conniver...and hires the local trouble-maker Brom Broeck (Nelson Eddy) to work for him instead of spending his time printing pamphlets demanding freedom. Eventually, Broeck realizes the Governor was just using him and the pair spend the movie fighting for the same woman and trying to outwit each other.
The story is purely tongue in cheek entertainment....fun as well. While the story is from a second-tier studio, the songs are fun, the acting nice and the story engaging. Well worth seeing...even if it's a lousy history lesson.
By the way, the real Peter Stuyvesant wasn't so much corrupt as a martinet who managed to make the citizens of Dutch North America thoroughly hate him. When the English arrived to seize the colony, Stuyvesant wanted to mount a defense...and the people of New Amsterdam quickly surrendered and seemed happier under English rule.
Also, it's not at all important but the film refers to Broeck being placed in the stocks for punishment, but the device was actually called a 'Pillory'. Stocks were for the feet...the pillory for the hands.