Taking Sherlock Holmes out of his element in Britain is a pretty bad idea. If he isn't able to use his encyclopaedic knowledge of the different dirt types of London, then he becomes something less than Sherlock Holmes. This film does seem to know this, and so it decides to work as more of an adventure story than a mystery, but this leads to other, more major problems - the audience knows what is happening far before Sherlock Holmes does. This is never a good idea. It isn't even that the mystery is so obvious that the audience can work it out easily, it's that we are actually told what is happening, as Holmes tries to work it out. This is poor form for a Sherlock Holmes film.
Another odd thing about this film is the cinematography - it is often highly inventive and interesting - when Basil Rathbone isn't on screen. When he is on screen, it's just boring point-and-shoot type stuff. Could Rathbone really not be arsed to wait for interesting camera setups? Or was it too expensive to experiment with the camera when there was a star on set? At a guess, I would say "yes" to both of those questions.
I would also like to take some time in this review to analyse Nigel Bruce's protrayal of Dr. Watson, partly because he was the only thing that was consistently interesting about this film. To Holmes purists, it has usually been regarded as somewhat annoying that Watson is portrayed as this bumbling moron, but let's be honest with ourselves - how the hell else do you portray Watson on film? The whole point of the character in the books is that he is basically just there to observe and humanise the Holmes character. He is the reader's in into the world of Holmes - the one we can all relate to, and that tells us how we are supposed to react to the craziness that he sees. He is our Alice, or our Luke Skywalker. But in the films, that doesn't really work. Because he isn't narrating things, we have no real way of properly experiencing what he is experiencing, and so he just becomes sort of... useless. So there are two solutions that filmmakers tend to use. They either just diminish the character of Watson, make him just sort of stand there, give Holmes someone to talk to without having any personality of his own. Or, they can turn him in to a bumbling fool, make him comic relief, so that the audience can sit there thinking, "well, I may not be as smart as Holmes, but I'm certainly not as dumb as Watson." This latter solution may seem somewhat disrespectful to the books, but when you have a performance that is as fun as Nigel Bruce's, frankly, I don't care.