How do I determine if a paper has undergone anonymous peer review of its statistical analysis?
Let's tease apart two issues here:


Has a paper undergone peer review of its technical content (which will include the statistical content)?
Should you believe the statistics in the paper?


If it's in a well-respected peer-reviewed journal, then you can assume that it's undergone reasonable peer review.  That means it's unlikely that the content is blatantly and obviously crazy, and that in fact it's likely to be fairly solid.  It does not mean, however, that it is correct, particularly when it comes to something as subtle and frequently mis-applied as statistical analysis.

Bad statistical analysis is extremely common in every field of science, for a number of different reasons. Ignorance is a really big one, though, and one that's likely to be shared by the peer reviewers.  Thus, if you want to know whether to trust statistical analysis, you need to look at it yourself.