In most episodes (including the pilot) J. B. Fletcher's first novel is referred to as "The Corpse Danced at Midnight", in this episode it is referred to as "The Corpse Danced Alone". Jessica even calls it "The Corpse at Midnight".
When the police lieutenant puts his hand in the water, his shirt cuff is suddenly unbuttoned and his jacket sleeve pushed up.
The Russian egg-hunter tells Jessica he represents "Nevsky Publishing, Moscow". This doesn't make sense, as the word "Nevsky" is directly synonymous with St. Petersburg. It means "of/on the river Neva", which runs through the city.
The killer wore a buttoned up shirt with a bow tie. Even with the second button torn off in the struggle, there's no way that the medallion worn on a chain around his neck could have been torn off.
Juvenile records are sealed, so there's no way the girl's father could have known about her boyfriend's previous crime.