I realize nobody but Wolfgang cares, but given n songs mentioning dates and given all the assumptions Wolfgang made (which as Bill points out are certainly false), the probability that every day in the year is covered is

[1-(364/365)^n] * [1-(364/365)^(n-1)] * [1-(364/365)^(n-2)] * ... * [1-(364/365)^(n-364)]

where the * represents multiplication and the ^ raising to a power. (To include Feb. 29, make the obvious adjustment.)

The first factor is the probability that the n songs cover Jan. 1, the second factor is the probability that the remaining n-1 songs cover Jan. 2, and so to the end of the year.

If you feel like simplifying that any further than doing the common denominator in each factor, I'd be interested in the answer. This is why God gave us (but not me) algebra software.