Analyzing a client site for any history of Google penalties is a time consuming process which requires a lot of manual work, cross referencing traffic drops with known algorithm changes. There are some companies that offer this as a paid service, but the price they are asking is not always justified. Finally, I was able to find a good FREE Google penalty checker that employed the same idea, analyzing your traffic and comparing it to known algorithmic changes and chatters in the SEO community.
Analyzing the Google Analytics data for a website, you can see the traffic changes since the release of a specific Google update. Basically, if the traffic is up, it means that the update liked your site and if it is down, well you got slapped. The one page report, will not give you a 100% accurate conclusion on weather your site is hit by a specific penalty, but it will give you hints where you should pay more attention and what you are doing right and wrong. If Penguins improve your traffic and Pandas drop it, well it is pretty much self explanatory.
You can test the free Google penalty checker here: