The European Union is implementing a new regulatory framework for nutrition and health claims (HCs) that will greatly impact the communication of health messages on foodstuffs. In particular, approved HCs will be included in a positive register of generic claims. In the currently available literature, assessment of the relevance of HCs has mainly been related to scientific substantiation, and the issue of relevance in terms of public health has tended to be overlooked. Interestingly, the new regulation states that claims must be well understood by the average consumer. This article delves beyond the issue of scientific substantiation of claims and reviews possible discrepancies between consumer perception/understanding of HCs and the public health nutrition reality, which can confuse or mislead the consumer and ultimately impact public health nutrition. Six pitfalls are described herein and a comprehensive overview of the critical examination of any HC is proposed.