Mary Suetopia: The Hapans are an incredibly wealthy and powerful matriarchal society of beautiful women (served by beautiful men) who possess an unbeatable navy. The book goes to great lengths to remind us of these facts (later books avert this trope by playing up the unpleasantaspects of Hapan life and downgrading their technology to galactic norms.)
Narm: The subplot with Threepio trying to "prove" that Han is actually King of Corellia. Of course it is also played as this in-universe, particularly once the truth comes out about his supposedly regal ancestor. (This also becomes Hilarious in Hindsight when you realize Thrackan Sal-Solo is descended from this same Con Man.) Also, one alien vessel is given a name which is essentially a transliteration of Blowing a Raspberry.
The funniest part is that Threepio might actually have been right, as the Corellian Sector was ruled by the Solo family for a long time before a republican revolution overthrew the kings.