"God Save the Queen" is doggerel, but as doggerel it has its points. Many people have admired "Confound their politics, / Frustrate their knavish tricks", tho no doubt having different "enemies" in mind. But even better, IMO, is the climax:
May she defend our laws
And ever give us cause
To sing with heart and voice
"God save the Queen!"
The spectacle of subjects praying for Divine intervention to make the sovereign mind her business (with, even, a hint of warning in "give us cause") is a splendid one.
As to the *worst* song, it would be a terrible task to pick out the worst one from the hundreds of thousands of bad ones that are lumped at the bottom. Among the songs *that are sung at participatory sings*, there are a few that instantly make me wish I were elsewhere, but I have commented on them in the appropriate threads.