Why is using $p$-values bad? I was reading this article on nature, and it seems to suggest that using $p$-values is bad, yet most of the textbooks I have read about statistics use $p$-value as a method of rejecting the null-hypothesis.  I am confused, why would textbook teach a method if it is so flawed.
 A: The short answer is that a $p$-value is not "bad."  It's not a flawed method.  The problem is one of interpretation, not meaning or utility.  Yes, if you ask a Bayesian, you might get some legitimate criticisms of $p$-value and the frequentist approach of hypothesis testing.  But Bayesian methods are not without their criticisms, either.
Non-statisticians commonly misunderstand the $p$-value; in particular, they tend view its size as a sort of absolute (and unconditional) measure of the truth of the alternative hypothesis.  But that's not a flaw of the method itself, but rather, a flaw in the way it is understood.  It's like claiming calculus is flawed because one doesn't understand the meaning of a derivative.
A: why would textbook teach a method if it is so flawed
This is a fascinating issue. Google will give you a lot of interesting stuff to think about.
http://ist-socrates.berkeley.edu/~maccoun/PP279_Cohen1.pdf
http://www.apastyle.org/manual/related/kline-2004.pdf
A: P-values are OK, but as heropup pointed out, they are easy to mis-interpret or "hack" as the article points out. A better approach (and the one I use almost exclusively), is to provide a point esimate and an interval around this estimate (e.g., confidence interval). 
The issue of how reproducible "significant" findings are. That is, what is the probability of a replicate study being signifiant given the first study was significant $P(p_{rep}\leq0.05|p_{initial}\leq 0.05)$? This issue has been stuided for some time and the controveries are not new. For a fairly recent quantative study of this issue, take a look at this article: http://www.tandfonline.com/doi/abs/10.1198/tas.2011.10129. They showed that the boostrap distribution of p-values for a particular dataset show that in some cases, p<0.05 is quite common, while in others, the p-values can be unusually concentrated around higher values like 0.7. 
Basically, the error comes from not recognizing tha the p-value is a statistic not a parameter. As such, it has sample to sample variability, and that variability is NOT based on the null hypothesis but the actual underlying distribution of the data. Now, IF the null hypothesis is true, then the p-value will have a uniform(0,1) distribution, but if not, then all bets are off and the p-value have almost any distribution whose support is [0,1]. 
As as concrete example, I recently analyzed someone elses study where they performed 50+ hypotheses tests, each with a different sample, but same null hypothesis and cutoff. When I looked at the distribution of p-values, they did NOT follow a uniform distribution but were skewed HIGH, looking like a triangular distribution as opposed to a uniform distribution...YET, the analyst concluded that the null hypothesis could not be rejected because none of the tests yeilded a significant result. Well...a goodness of fit test (pick any one) on the distribution p-values vs uniform(0,1) suggested otherwise, with the goodness of fit test p-value being <0.001.
