As I think I mentioned, it's a little-known fact these days that before 1950, it was far more common for Sherlock Holmes movies to update the setting to the present day than to set them in Victorian times. After all, the Holmes stories were still being published through 1927, so for the first couple of decades or so of Holmes cinema, it was a contemporary series. And so most films continued to treat it that way for the next couple of decades, the first two Rathbone films being the main exceptions (along with the 1916 silent film adapting William Gillette's stage play). It was only in the '50s onward, when a generation had grown up thinking of Holmes as a character from the past instead of the present, that it became standard for Holmes stories to be period pieces. (It's weird how total the transition was, though -- from mostly contemporary adaptations pre-1950 to exclusively period portrayals of Holmes post-1950, and then Sherlock and Elementary coming along in quick succession in the 2010s.)
So while the Rathbone-Bruce films did take their liberties, especially with Watson, in many ways they were more authentic than their modern reputation would have it. They had lots of neat little nods to ideas and details from the stories, like the paraphernalia found around 221B Baker Street and the bullet holes Holmes fired into the wall there. And Basil Rathbone was a superlative Holmes, aside from being, like Jeremy Brett after him, somewhat too old for the character as described in the stories (who was mid-20s in A Study in Scarlet and in his 30s for the majority of the canon).