What's the difference between the versions of Cards Against Humanity?
Changes to the base game are discussed here. There is also some additional information on this thread included photos showing old and new versions. 

Between the original and version 1.2, it seems like they got rid of a lot of cards that mention proper names. It seems that cards mentioning Glenn Beck have been removed in 1.3. The second post indicates that at least 8 black cards were replaced and 80+ white cards were changed (though some changes seem small) between the version that came out in early 2012 and the previous one. 

This page also has a link to a PDF file (must login) that lists some changes for the first expansion (v1.2 Changelog). Here is a summary:

A bunch of white cards were added:


A pluger to the face
The ooze
Clenched butt cheeks
Stockholm Syndrome
Salvia
Syphilitic insanity


Some white cards removed:


Appreciative snapping
Dancing with a broom
Good grammar
Pistol-whipping a hostage
Slow motion
The Fanta girls


A few minor corrections as well. 

A bunch of black cards were also modified:


Orig: My plan for world domination begins with _ / New: He who controls _ controls the world
Orig: Science will never explain the origin _ / New: Science will never explain _
Orig: Next season on Man vs Wild, Bear Grylls must survive in the depths of the Amazon with only _ and his wits / New: This season on Man vs Wild, Bear Grylls must survive in the depths of the Amazon with only _ and his wits