Critical thinking is as much about psychology as it is about logic. We are constantly tempted to overestimate our cognitive powers and underestimate our capacity for error. Overcoming this requires constant vigilance and self-examination.
For example, when we believe something or have an idea, our first thought is often to look for ways to confirm that it is true. This quickly leads to confirmation bias, or cherry picking of data. The appropriate thing is to look for ways to falsify it, but this does not come naturally. Also, when evidence is ambiguous, we tend to interpret it in a way that is most favourable for our own views. When evidence comes along that contradicts what we believe, we have a tendency to hold it to a higher standard of acceptance.
We also cut corners a lot when thinking: we rely on useful heuristics to save time, but this can often lead to blind spots. We also frequently overestimate the veracity of our memory and underestimate our susceptibility to suggestion.
As well as cognitive biases, we tend to suffer from motivational biases, such as wishful thinking. People are often quick to accuse others of wishful thinking, but the fact is we are all vulnerable to it. We also don't like to admit errors or change our minds about things, because we naturally tend to see this as an act of weakness, but it leads to entrenched positions and gets in the way of accepting things as true.
Another very common problem is that we tend to congregate with others who agree with us, which leads to reinforcement of what we already believe. It is always a good idea to spend more time reading and conversing with those whose views diverge from our own.
As to books, Steven Novella's audio book, Your Deceptive Mind, is good on the psychological side of things.