The current Dolphins throwback is the 1966 uniform and not 1972 - the main features that distinguish it are the wide stripes on the helmet, and the reverse piping on the pants (aqua-orange-aqua for 1966, orange-aqua-orange for 1972). I thought the helmet logo was a reference to the 1972 team, but it turns out they used both types in 1966:
There were many subtle differences over the years within the first three major uniform styles (1966-1986, 1987-1996, 1997-2011, 2012-now), and sometimes (notably in the Superbowl years) there were differences between players in the same game in regard to helmet logos and jerseys. For example, Kuechenberg's helmet logo in Superbowl VIII (picture 2 of the opening post), the sleves and numbers of Griese's & Csonka's 1971 jerseys compared to the others at Superbowl VII:
One of the other subtle changes to the Wilson made Jerseys (from 1988-1996, Russell Athletic began the second major incarnation of the jersey with the numbers moved to the shoulders and logo on the sleves with three stripes in 1987) was the change to block numbers and letters on the nameplates from 1994-1996:
One day I will have to start a thread here on all the subtle uniforms changes the Phins have had and how you can pick the year due to minor stuff like the color of the belt, font of the lettering, positioning of the manufacturer's logo...