No - I've just logged on to the main dropbox site via the Kindle web browser and have successfully managed to download mobi files in both the public section of my dropbox folders and from other folders with no issue.
If you are also logging into dropbox.com then I can only think it may be because your Kindle is not on the 3.0.3 firmware - or that it is maybe an intermittent glitch which will be harder to catch.
Note that I've just downloaded files with a .mobi extension and not any other file types.
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