Yes there is the most famous is that of Egon Kisch, a communist who attempted to enter the country in the late 1930s. Now as a man of some intelligence he spoke many languages fluently including English so when the first test was given he passes with ease. However the legislation gave no limit to how many times you needed pass the test. In fact the only rules given were as follows.

"Any person who when asked to do so by an officer fails to write out at dictation and sign in the presence of the officer a passage of fifty words in length in an European language directed by the officer" would not be admitted.

As a result he was given the test several times passing each one until the government found a language he did not know. That language been Scots Gaelic which was barely spoken to the point were the person giving the test could barely speak it. Egon failed this test and was excluded, however this lead to a huge controversy in Australia and was really the beginning of the end of the test.

So to summarise there was nothing that was fair about the dictation test there is no record of an undesirable entering the country by passing the test as it was designed to be impossible to pass.

To give an idea here are some statistics on the use of the test. The Dictation Test was given 805 times in 1902-1903 with 46 people passing, and 554 times in 1904-1909 with only six people passing. After 1909, no person passed the Dictation Test.