Someone who puts their “best foot forward” must, logically, have three or more feet.
Although this is a very common phrase (the title of a 1943 Lucille Ball film, for example) it is, at least for humans, grammatically incorrect.
“Best” is the superlative form of the adjective “good” and superlatives are used to refer to one item from a group of three or more. The comparative form of the adjective – “better” in the case of good – should be used to refer to one item from two. So, the phrase should be “better foot forward” if talking about a biped. Only a creature with three or more feet – a centipede for example – could actually put its “best foot forward”.
The general point applies to all comparative and superlative adjectives. You can’t be the fastest runner in a race of two, for example, only the faster.
Here are some examples of this usage around the web:
There are hopeful signs. On Wednesday he conceded he couldn’t get the economy going again simply by blaming the Democrats, up to now his favorite response to the recession. And he said yesterday that he would run “on my whole record,” suggesting that he may put his best foot forward instead of merely stepping on his opponent’s. – NY Times
The Bears arrived in St. Louis without their best pass rusher — Pernell McPhee stayed home with a knee injury — and yet they left with a convincing TKO of a potent Rams offense. – LA Times