Slate has a story on Baby Einstein and the at best ambiguous evidence supporting its claims to enhance infants' mental development. The American Academy of Pediatrics recommends no TV for kids younger than 2 years old, and the concern is that the shows crowd out activities like unstructured play that are superior for mental and physical development.
As the Slate story notes, in May, the Campaign for a Commercial-Free Childhood (represented by Georgetown Law's Institute for Public Representation) filed a complaint with the FTC seeking to have Baby Einstein and Brainy Baby investigated and enjoined from making unsubstantiated claims. This is an obvious case where government can do what Lanham Act suits won't: no competitor has any incentive to challenge the basic efficacy of baby videos. Likewise, consumers are unlikely to have the resources or the information to challenge these claims.
FTC rules require substantiation for advertising claims, unlike the private actions that require plaintiffs to prove falsity. The big question here is whether any research-based substantiation is required for claims to enhance infants' mental development, or whether anecdotal testimonials suffice. Baby Einstein and Brainy Baby have plenty of satisfied customers, but the research all goes the other way, and it's certainly possible that customers' babies would be as smart or smarter if they'd been playing with blocks instead. For health claims, the FTC requires more rigorous substantiation than for ordinary claims, in part on the ground that consumers expect that health claims are backed by scientific evidence. Are "brain development" claims similarly likely to be interpreted as claims that controlled/replicable studies show that the videos are good for babies? I would say yes, especially given parents' susceptibility to claims that things are good for their babies.
Full disclosure: as a parent of an infant, I own a Baby Einstein video, but I've never opened it -- like other anxious parents, I'm vulnerable to lots of pressure and advice and prone to second-guessing. It would be awfully nice if I could guarantee him admission to the college of his choice by careful video selection now. My son also watched a Sesame Beginnings DVD once, but he showed little interest in the Muppet Babies, and we haven't been back.