The author, Gershoff, does a review of previous spanking studies. A meta-analysis (summary of previous studies) says that spanking is correlated with aggressive and antisocial kids. It doesn't say whether the kids were spanked because they mishaved, or if they misbehaved because they were spanked. It didn't say whether mild to moderate spanking is good or bad. But it did say that spanked kids were more likely to do what they were told.
From this, she concludes that psychologists should recommend against spanking.
Some of the criticisms are:
Gershoff concedes the gist of these criticisms, and defends her work. IMO, these criticisms are devastating. Her data can be used to support spanking as much as it can be used to criticize spanking. Her data show that kids who misbehave get punished, and getting punished results in better behavior. Only those severe child abuse has adverse consequences.
Gershoff's work just seems like ideology masquerading as science. Some people are ideologically opposed to spanking out of a belief that abolishing spanking will promote a nonviolent society. So they want to claim that spanking is harmful. But that cannot find any evidence that spanking is harmful, so they combine spankers with child abusers and then look for evidence that child abusers are causing harm. The whole analysis is bogus.