It is of course possible to do both frequentist and Bayesian statistics badly. I would say bad frequentism comes when one fails to realize that standard frequentist methods tell you the probability of the data given a hypothesis, when what you really need to know is the probability of the hypothesis given the data. Bayesianism at least starts right out with the latter approach, so it avoids the former (unforfunately all too common) error.
Bad Bayesianism, OTOH, I would say comes when one fails to realize that Bayes' rule is not a drop-in replacement for your brain. You still need to exercise judgment and common sense, and you still need to make an honest evaluation of the information you have. You can't just blindly plug numbers into Bayes' rule and expect to get useful answers.