It is still unknown exactly why the couple broke up in between Season 1 and 2. It is thought by fans that it was because they reminded each other of Beth too much. Quinn has also admitted, to Sam in Duets, that she recognized the feeling of "needing someone," hinting that was what she felt with Puck after Beth was born.
They both got haircuts that changed their appearance (Puck shaving his mohawk off and Quinn cutting her hair into a pageboy cut)
Puck is the only boyfriend Quinn didn't cheat on and was willing to have sex with.
The only time Quinn wanted to keep Beth was when there was a possibility of her and Puck raising her together, as a family. Sadly, her hopes were dashed when Puck was caught sexting with Santana, leaving her heartbroken.
In the series, Quinn is Christian and Puck is Jewish. But in real life, Dianna is Jewish and Mark is Christian.
Never had a duet.
In a deleted scene in Grilled Cheesus Quinn said "I really like you." and Puck replied "Just let me get to third base a couple days a week."