Abusive Parents: The main character of "All the Stars in Texas" mentions that his tagalong girl had a crooked father who was both this and The Alcoholic. The main character shot him dead in disgust and took her along.
Does This Remind You of Anything?: Averted in the unofficial "Whipped Cream" video. The things they put whipped cream on become increasingly ridiculous, and its done with with such seriousness, that by the time they're putting whipped cream in passerby's mouths and each other you're too busy laughing to be reminded of anything.
Mood Whiplash: The Broken Bride Album, period. Mainly "The Lamb and the Dragon". Its starts in a hard-rock metal-like solo, then turns western-ish. With whistling. And then the western tune gets hard-rock-ified. Then a depressing solo by the Traveler. It's awesome.
To a small degree, Skeletons on Parade. It initially sounds like a group of undead laughing at Halloween and planning a nice parade, but later the shift from jazzlike to metal makes it darker as they talk about overwhelming the living in a small town. It finally reaches creepy with the line NO ONE GETS AWAY. Then in comes the last chorus which is nice and serene.
The Mourning After: the traveler in "Broken Bride" has a bit of a problem letting go of his late wife.
Silly Love Songs: Even the played straight love songs are quite silly, and maybe all the sweeter for it. Straight examples (i.e. not Stalker with a Crush songs, for example) include "Anything for You", "Manta Rays"
Stalker with a Crush: Go-Getter Greg. "Haven't seen you at the pool since the barbeque! Not that I've been checking..."
Arguably, the narrator in "Hum Along", and for a much much darker example, "The Horror of Our Love"
Silent sleeper, I've been inside your bedroom/I've murdered half the town/left you love notes on their headstones...
Troperiffic: One review of You're Awful, I Love You pointed out that Andrew (who writes most of the lyrics) seems to write from the point of view of someone who learned everything they know about relationships from watching TV (if anyone recognizes this and knows a link to the review, please provide)
Tsundere: "Love Me Dead." Best summed in five words: