One of the more common irrationalities I see on the internet is the sin of foolish consistency. i.e. people post something without a lot of thought and then when evidence or arguments arise which undermine their statement, they are overly dismissive because they do not want to appear inconsistent.
An excellent way to improve one's skill as a rationalist is to identify one's strengths and weaknesses, and then expend effort on the things that one can most effectively improve (which are often the areas where one is weakest). This seems especially useful if one is very specific about the parts of rationality, if one describes them in detail.
In order to facilitate improving my own and others' rationality, I am posting this list of 11 core rationalist skills, thanks almost entirely to Anna Salamon.