Regulations that affected car styling the most in the first half of the decade had to do with bumpers. This link mentions a 1971 regulation taking effect for 1973 models that dealt with collision damage, and bumper designs had to be adjusted to protect more parts of cars. The next year, regulations dealt with placement of bumpers and the impacts they had to be designed to deal with, requiring even larger protection systems.
These regulations could have been more easily dealt with if designers were allowed to implement them when a new design was launched. Unfortunately for stylists and engineers, designs already in production had to be modified. The result often was heavy, awkward-looking bumpers placed on designs originally featuring far less protection. As time went on, bumper impact criteria became more easy to accommodate, and protection systems on today's cars are hardly noticeable.
Below are some examples of Detroit cars and how they coped with the new rules.