Picard says that they will be entering orbit in 6 hours. But, just before that, there is an establishing shot of the Enterprise already approaching the planet and its two moons. It should be minutes, not hours before they are in orbit.
When a renegade ship attacks the shuttle carrying the ambassador and Commander Riker, Captain Picard inexplicably does nothing to protect the shuttle and his first officer. The Enterprise could easily disable the attacking ship without destroying it, yet all the Enterprise does is lock a tractor beam onto the shuttle, effectively allowing the shuttle to be a sitting duck until it is within the Enterprise's shield bubble. However, Riker's shuttle was already a sitting duck as the controls were down, and the Enterprise firing on the alien ship would surely inflame an already precarious situation. Once the Enterprise locked onto the shuttle with the tractor beam, the alien ship immediately withdrew - which was the desired effect.
Odan is identified as a Trill, the doctor states that there is not a lot of information on Trill anatomy. This clashes with the 30+ years that Benjamin Sisko is acknowledged as having known Curzon Dax. Surely Starfleet would have more information on the Trill.
On the other hand, the Trill may not initially have been forthcoming to other races about their conjoined nature. (As close firneds, Curzon may have confided in Cisko.) There have been many examples of Star Trek races not wishing to talk about aspects of their culture to 'outsiders', e.g., the Vulcans about pon farr or the Klingons about why some of them do not have ridged foreheads.