I noticed that my ‘64 quarters all have very weak appearing tails on the eagles. It doesn’t look as if the surrounding areas of the coins are as weak nor do I see obvious signs of damage beyond what might be expected on a 56 year old silver coin. Am I imagining this. Coincidence? Typical for this coin? Just wondering.
Wing tips are not as sharp as they should be either. The tail feathers are probably the result of a weak die and circulation. But, the tail feathers on the Washington sometimes give an optical illusion of weakness if held at different angles. I looked at several of my 1964 BU quarters and they have varying degrees of what you notice on yours. I agree with @Robert Ransom above.
There was an acute coin shortage during that period which had the mints pushing coins out night and day. Many die pairs were pushed to the limit. Back then, the overall prices were much lower, and coins really did matter.