In Manny's original video application, he does a cover of the Broadway musical, "Hamilton," which was created by Lin-Manuel Miranda, who appeared in Good Cop Bad Dog (2011) as Stella's original owner who proposed a bad business idea to Jay.
When she meets Rainer Shine, a pun on "rain or shine", Haley asks if it's really his name. In the Castle (2009) episode "Cloudy with a Chance of Murder (2012)", Richard Castle, also played by Nathan Fillion, wonders the same thing about a weather girl with the last name Fog.
In the revelatory Scrabble game, a look at the board shows that many of the word groups are disconnected. That would be against the rules.
Episode name is a pun on Wuthering Heights (either the book by Emily Bronte or the song by Kate Bush).