At first, Mia's line "and when faced with tribulation, I think of my own inspiration./He taught me to always hold my stance" in the song Justice for All seems to be just a line they put in to make a rhyme and give Phoenix the chance to make a callback in the reprise... then you realize that she's singing about Diego Armando.
Edgeworth's defense of Cody in The Samurai Always Wins makes a lot more sense when you consider the fact that Edgeworth was involved in a murder case and may have had to testify when he was Cody's age.
None of the solutions to the mysteries are entirely contained in the songs. Therefore, in order to find out the full story, you have to either see a performance of the full show or (more likely) buy the game. It's a way of making it up to Capcom for using their characters, by advertising the game they come from!
In 600,000 Volts, von Karma sings "Now your life's depending/On giving that letter to me" when he tries to threaten Phoenix and Maya into handing over their evidence. It might seem like just a way to intimidate them but then, remember that he did already kill a defense attorney who defied him. Makes you wonder what would have happened if the tazer didn't just knock the two of them out...