Consider these ideas while writing a critical analysis:
Can you solve the Hardest Logic Puzzle in the World?
Guide to Thinking Critically About What You See on the Web:
Created by Ithaca College, this training tutorial is designed to explore questions relating to using the World Wide Web as a research tool and to challenge you to use the Web wisely and efficiently.
A fallacy is an argument that uses poor reasoning. Check out some of these websites devoted to the study of fallacies and that discuss some of the most common fallacies:
The Fallacy Files by Gary Curtis
Logical Fallacies by Purdue OWL
Fallacies - Internet Encylopedia of Philosophy
Fallacies - Writing Center by Univ. of North Carolina