The sentences that do not use brackets correctly are:
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Dr. Janusch began his experiments during the 1920s [See pages 33 and 34], but the turning point in his work came in 1935. (This sentence improperly uses brackets for a reference to a source, which should typically be in parentheses.)
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The feature of the day is the Hubble Telescope movie of Neptune [found on the website of the National Aeronautics and Space Administration [NASA]). (This sentence has mismatched brackets. There should only be one type of bracket used at a time.)