These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
"Pressure", "Allentown", "Uptown Girl", "Tell Her About It", "My Life", "Big Shot", "Piano Man", "Just The Way You Are"—-he is a king of ear worm-writers.
No mention of I Go To Extremes? That sound is mindblowingly catchy.
"Only the Good Die Young" is one of the catchiest songs of all time.
Growing the Beard: His 1973 album, "Piano Man", containing such classics as "Captain Jack", "The Ballad of Billy the Kid" and of course Piano Man.
Harsher in Hindsight: "Miami 2017 (Seen The Lights Go Out On Broadway)" is about the violent destruction of New York, despite being written before 9/11/2001. Joel sang the song at a number of 9/11 tribute concerts to defy the trope.
More recently he sang it again at an NBC benefit concert telethon for victims of Hurricane Sandy. He even changed one line of lyrics to reference the serious damage sustained by Staten Island in the storm.
Painful Rhyme: "Uptown Girl" features both the world/girl combination, as well as walkin/talkin.
Paranoia Fuel: "Movin' Out" is a mostly harmless song, but the sound effects of screeching tires can be heard in the middle of the song... which is not exactly a kind thing for drivers to hear on the radio.
Squick: The "instant pleasuredome" line in "You're My Home."
"Captain Jack" counts as well.
Tear Jerker: If you live in New York—or really anywhere in the New York metro area—then "Miami 2017 (I've Seen the Lights Go Out On Broadway)" can definitely be this.