The following is a quote from the June 22nd 2000 Awake article 'do not be a victim of propaganda!'
Ask questions: As we have seen, there are many today who would like to ‘delude us with persuasive arguments.’ (Colossians 2:4) Therefore, when we are presented with persuasive arguments, we should ask questions.
First, examine whether there is bias. What is the motive for the message? If the message is rife with name-calling and loaded words, why is that? Loaded language aside, what are the merits of the message itself? Also, if possible, try to check the track record of those speaking. Are they known to speak the truth? If “authorities” are used, who or what are they? Why should you regard this person—or organization or publication—as having expert knowledge or trustworthy information on the subject in question? If you sense some appeal to emotions, ask yourself, ‘When viewed dispassionately, what are the merits of the message?’
Although criticle thinking isn't specifically mentioned in the article, some critical thinking skills are discussed here.
I've used the reasoning in this article to good effect with some of my family to show that looking at the organization's real history is not 'critical' in a bad way.