It's a common misconception that the '72 Dolphins are the only team ever to have a "perfect" season. It was actually accomplished four other times as well--the 1920 Akron Pros, the 1922 Canton Bulldogs, the 1923 Canton Bulldogs, and the 1929 Green Bay Packers.
Now, it's important to note that all of these teams have very noteworthy asterisks attached to their perfect records:
First of all, this was before the creation of a playoff system--the championships were simply awarded to the team which finished the season with the best record.
Secondly, all of these teams did have games end in ties during their "perfect" seasons--present-day record books show that the 1920 Akron Pros ended the season 8-0-3, the 1922 Canton Bulldogs were 10-0-2, the 1923 Canton Bulldogs were 11-0-1, and the 1929 Green Bay Packers were 12-0-1. However, at that time, the league did not include ties in the standings--at all. If two teams came into a game with a record of 2-0, and they played to a tie, both teams finished the game with a record of 2-0, not 2-0-1. And therefore, both teams continued to have a perfect record. It wasn't until 1972, when the Dolphins were making a run at their own potential "perfect" season, that the Dolphins petitioned the league to declare those other seasons "imperfect" because of the ties, and to add those ties to the record book standings. The NFL, in an attempt to help build press surrounding the Dolphins' season, agreed.
But should they have done so? When those teams were in games which appeared headed toward ties, they knew that they could play for a tie and still maintain their "perfect" record. They therefore had no reason to try to avoid the tie. Per the rules those teams were playing within, they had perfect seasons. When they opened their newspapers the morning after the season ended, the standings showed all four of them with perfect, unbeaten records. (Which means that while the "perfectness" of these four seasons can be debated, there is no arguing that the '72 Dolphins claim of being the only team to finish a season with a perfect record is completely false, as the records of these other four teams were perfect WHEN THEIR SEASON ENDED, until the Dolphins 1972 request was granted.)
Claiming now that those seasons weren't perfect is a bit like claiming that the Dolphins weren't unbeaten in 1972 because in one of the half-dozen games they played that year that were decided by a touchdown or less, an officiating error was made that would have been reversed by instant replay and resulted in the Dolphins losing that game. That's completely irrelevant--there was no instant replay in the rules at the time, and the Dolphins therefore were perfect according to the rules they had to go by. Similarly, the four teams in the 20's with perfect season were perfect according to the rules they had to go by at the time, and that accomplishment therefore should not have been stripped from them.