The O'Briens' baby is born without an umbilical cord. This could be an effect of the odd circumstances of its gestation.
When Odo pours the baby changeling out of the glass, a residue of the same color remains in the glass, due to the production substance used to depict the changeling. Changelings are a whole entity, and part of them (even a residue) can't be separated.
When the the computer notifies Odo the Changling life signs were fluctuating he tells it to notify Dr. Mora to meet him in the lab. Odo prior to this told Quark Dr. Mora went to bed. Well Dr. Mora must be sleeping in the lab because he was there before Odo arrived and already knew what was happening.
At the very end, when Odo changes into the hawk and flies above the promenade, just before landing, there is a director's chair visible on the lower level on the right and appears to have a script on the seat. This is directly adjacent to 2 extras walking on the left.
Dr. Mora refers to the Cardassians but pronounces it "cah-dashuns"