One of the biggest offenders in the use of superscripts is Microsoft(R) Word for two reasons: One is that this feature is a default. The other is that the feature is difficult to find and change. As a graphic designer, I receive text files from customers that contain two bothersome uses of superscripts in ordinal numbers.
One is that the superscript text is so small that it does not print well, particularly when the normal type is small.
The use of normal size text works just fine.
The other is that the use of superscripts in date formats is inappropriate.
Note that in the first date, the comma looks peculiar. Also, if care is not exercised, the year may also become a superscript.
The correct form is June 1, 2015
My advice: Turn off this feature in the auto correct options.
Go to file/options/proofing\AutoCorrect Options and uncheck the ordinals option.