For the most part they will try to make it a polarizing document about politics. So, the analysis will lean toward how the "liberals" or "conservatives" have an advantage from what is in it. It will also try to use other political figures (e.g. Obama vs Bush) as a way to frame the argument. This is the WRONG way to approach or interpret the document!
Another thing you don't want to pay attention to is comments made out of context.
Lastly, avoid simplifications of the principles the Pope is giving. He is not trying to solve the world's problems, but point out higher-level issues.
The Pope is teaching about the human person and the dignity of life. He is trying to wrap principles of rights & social responsiblities together with the public good and the duty of governments and economic systems. Ultimately it is about God and man, not "right" and "left".
If you want commentary about it, then be a bit patient. Good commentary on deep thinking will not be pumped out in a 12-hour news cycle. But, if you want the first reactions that I think are best, then here are a few of them:
- Jimmy Akin shares some of my warnings and has some of his own about what to look for.
- George Weigel does his regular bang-up job of quick analysis. UPDATE - on second thought this isn't a very good analysis by Weigel. I didn't read the second page of the article and there is too much conjecture.
- The Acton Institute also has some good commentary.
- Fr. Fessio also has some good thoughts.