What government regulations affect the fashion retail industry and retail clothing stores in particular?

For purpose of this question, we will discuss regulations separate from any general criminal law. Regulation of business usually serves the purposes of protecting the customers (consumers) of that business, protecting the employees of that business, and/or protecting society in general from potential adverse impacts arising from that business’s operation.
To keep it simple, consumer protection regulation requires that (a) products be safe to use, (b) key information about the product is accurately provided to the consumer before they buy, and (c) terms for payment, refund, and defect or problem resolution be considered “fair.” In fashion retailing, the most salient regulations require proper labelling (both in terms of fiber content, care instructions, and place of manufacture; see the link for OTEXA requirements below) and product safety (in terms of the dyes and fibers and their safety for use). This latter point may include flammability standards, especially for apparel marketed for infants and small children. Note also that the place of manufacture information may be used by some consumers to avoid supporting textile industries in foreign countries which engage in practices which those consumers may consider inappropriate or unethical (e.g. child labor). In this latter capacity, the regulation is furthering the aim of protecting the societies in which the apparel is manufactured.
As far as employee protection is concerned, fashion retailing in most US locations is governed by the same laws and regulations covering any retail business. For the most part, these regulations are national in scope, and cover such things as working hours, minimum and overtime pay, and worker safety (OSHA standards).
Finally it is important to note that many of the purposes of regulation are in fact accomplished through the adoption of industry standards and practices. That is, fashion retailing, like most other major industries, works to avoid overt government regulation by “self-regulating” through trade associations and industry SOP. An example of this is industry moves to foster use of sustainable fiber technologies (such as sustainability in cotton agriculture).
https://www.cpsc.gov/content/file-error