I was asked to review a commentary about studies involving remote healing (which includes prayer studies as a subgroup). It is not available yet on the web, but I'll try to link to it when it becomes available. One of the documents that this commentary did refer to, however, is available on the web.
Warning Signs in Experimental Design and Interpretation. Peter Norvig, norvig.com/experiment-design.html
This is a good commentary, but it falls into a philosophical trap that plagues most of the discussion on how to critically evaluate research, including (I have to admit) some of my own commentaries. See my Seven Deadly Sins of Researchers page, for example.
The problem with a checklist of mistakes is that it forces you to view the world in black and white. The checklist is a series of yes/no questions and if you answer all the questions yes, then the study is valid. Or maybe you are a tolerant person, and your rule is that if you answered half of the questions yes, then the study is valid. If a study fails to meet your criteria (one or more no answers, more than half no answers), then it is invalid.
There are times when we need black and white rules, but here these rules serve you poorly. In my opinion, there is no such thing as bad research (excepting unethical research, of course). Rather, the only thing that is bad is pretending that your data is making a stronger statement than it really deserves to make.
Rather than thinking of flaws in a research study as mistakes, think of them as factors which weaken the persuasiveness of the article when they are occur. They move a study from gray towards dark gray.
Alternately, when the researchers do something good, that does not immediately confer a certificate of acceptability on the study. Positive factors merely strengthen the persuasiveness of the study. They move the study from gray towards light gray.
There are times when you need black and white rules. For example, if you are conducting a systematic overview, you need a clear dividing line between those studies of sufficient quality to be included in the overview and those studies of insufficient quality, which need to be excluded from the overview. But in most situations, black and white rules are too simplistic.
I knew a statistician who refused to work on any research study that wasn't randomized. He felt that non-randomized studies were so compromised that to provide any help was to encourage bad research. That's his prerogative, of course, but it struck me as a bit elitist (and also a bit impractical). Our goal as statisticians is to present the data fairly and make sure that researchers (and the readers of the papers that they publish) understand the strengths and limitations of the findings.
In my book, I included a section at the end of most chapters stating that a certain concept was overrated. In Chapter 1, I mentioned that randomization was overrated, in chapter 2 it was intention to treat analysis, in chapter 3 it was blinding, and in chapter 4 it was biological plausibility. One of the reviewers of my book roundly criticized me for saying that randomization was overrated. It was like I was betraying my profession. But my point was not that you shouldn't randomize. Rather, it was that randomization does not confer on a study an immunity from criticism. Randomized studies have serious problems that are underappreciated.
There's another important issue to remember here. Studies are designed in a complex environment with a mix of competing demands. If you were studying the positive influences of breastfeeding on the health of a child, you would not normally randomize this type of study. First, it is a mistake to ask half of the mothers to forgo something that is known to benefit their children, even if our knowledge of all of the dimensions of benefit is still somewhat incomplete. Second, the decision to breastfeed (and for how long) is a very personal choice and we cannot easily control this in the way we control the dose of a patient's medication.
So, really, you could argue that randomizing a breastfeeding study is a mistake rather than failure to randomize.
What you can say is that our knowledge of the benefits of breastfeeding rests on an imperfect research foundation. Well, you could say that about our knowledge of anything, but what I really mean is that it rests on a shakier foundation than other areas where randomization is easy.
So rather than a list of "mistakes" I would much prefer a list of "factors that dilute the credibility of a research study". I like the word "dilute" because when you are dealing with a research area like breastfeeding where there is a lot of replication, a strong association, a plausible mechanism, etc., that can easily overcome the dilution of credibility that occurs when a study is not randomized, for example, or not blinded.
Now everyone falls into the black and white trap (including me). It is just so tempting to say "this is a bad study because the authors did not use blinding" or "this is a good study because the authors collected a large sample." If there is any message I could get across is that studies are not good or bad, but rather they vary in their degree of persuasiveness. Perhaps an adaptation of the famous George Box quote is called for here: All research studies are flawed, but some are still useful.