Science addressed the problem of How to (seriously) read a scientific paper by asking a group of Ph.D. students, post-docs, and scientists how they read the scientific literature. None of the answers will surprise you. The general theme is that you read the abstract to see if the work is relevant then skim the figures and the conclusions before buckling down to slog through the entire paper.
None of the respondents address the most serious problems such as trying to figure out what the researchers actually did while not having a clue how they did it. Nor do they address the serious issue of misleading conclusions and faulty logic.
I asked on Facebook whether we could teach undergraduates to read the primary scientific literature. I'm skeptical since I believe it takes a great deal of experience to be able to profitably read recent scientific papers and it takes a great deal of knowledge of fundamental concepts and principles. We know from experience that many professional scientists can be taken in by papers that are published in the scientific literature. Arseniclife is one example and the ENCODE papers published in September 2012 are another. If professional scientists can be fooled, how are we going to teach undergraduates to be skeptical?