Con Mixes markup (JSX) and JS
Con Large file size
React's react.min.js is 145.5KB in size. It's much larger than some other libraries that offer roughly the same features and it's almost the same size as some MV* frameworks such as Angular or Ember that offer more features out of the box.
Although, it should be mentioned that sometimes having a smaller library may force developers to reinvent the wheel and write inefficient implementations on features that React already has. Ending up with a larger application that's harder to maintain and/or that has bad performance.