An important part to me (as someone frequently trying to write a musical) is particularization. It takes more than writing a really beautiful song with great lyrics and a hummable tune. The song has to be tailored to the exact character, in the exact scene, in the exact story you are trying to tell. It's why jukebox musicals rarely work: the songwriter probably wasn't writing about anything, especially not whatever story the song is being duct-taped to.
It varies wildly from show to show, but reincorporation of melodies and leitmotifs really go a long way to creating a fuller, more unified score. Not only does it create a score that feels more like a complete work, rather than just a collection of songs, but it also rewards you for paying attention and listening to it multiple times.
As far as lyrics go, they pretty much need to be all perfect rhymes. Shows can work without perfectly rhymed lyrics, but they're the exception to the rule. Dave Malloy and Lin-Manuel Miranda get away with it because they're Dave Malloy and Lin-Manuel Miranda. I always appreciate when lyrics work in the vernacular of their subject matter. My favorite lyricist working today is Peter Mills. One of his shows, GOLDEN BOY OF THE BLUE RIDGE, is set in an Appalachian moonshiner's cabin, and works in tons of accented language and local dialect into the lyrics. Another of his, THE HELLO GIRLS, is about women enlisting as switchboard operators in World War I, and thus the lyrics are full of French phrases and military jargon. It shows a score comes from an artist that does their homework and cares about the people who are going to pay the closest attention to the score.
