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.
Tear Jerker: "Daddy". The singer himself starts crying. The entire song is about child abuse. He comes close to it again in "Kill You", about his step mom.
He also cries a little bit at the end of "Holding All These Lies." Of course, considering that Remember Who You Are was all about returning to form, one can't help but question if this bit of crying was genuine or done for the sake of nostalgia.
Pretty sure the crying in "Holding All These Lies" is genuine. An interview by Revolver reveals this is the first time Jon has cried during recording since Life is Peachy.
They also made a song called Tearjerker which was the final song for See You On The Other Side.