Diane is quoting Winston Churchill when she tells Sam that he's stupid and that she'll be sober in the morning.
The song Diane is singing to herself while drinking is Just Like a Woman by Bob Dylan.
In the opening scene, after the Cheers gang gives Harry The Hat a gift, he's shown wiping a tear from his eyes, as he does this, it's clear that the glasses he's wearing do not have lenses in them, as he slides his finger through the empty frames to wipe the tears.
The title is from the quote "How do I love thee? Let me count the ways", by the poet Elizabeth Barrett Browning.