The top of Ensign Ro's uniform that she gives to the little girl turns from a pullover-type garment to a jacket. Also, Ro's com-badge goes from the jacket to her shirt without her moving it.
In the first scene where Ensign Ro meets Captain Picard, the sliding doors to Picard's ready room bounce ajar when closing and the bridge remains visible in the gap until the camera change.
When Ro first speaks with Picard in his ready room, she unfolds her arms as she sits down. When the shot changes, her arms are folded once again.
When the away team is down at the Bajoran camp speaking to its leader, Ro's hands are clasped behind her back, except for one shot, where they are suddenly clasped in front of her. They return to being clasped behind her back for the rest of the scene.
Ensign Ro refers twice to her time in the stockade. Starfleet is an organization based on naval traditions and naval lingo. The "stockade" is an Army term for a jail or prison. The "brig" is where prisoners are kept in the navy, whether the sailors are at sea or on land. This is a detail the writers must not have been familiar with.
It is suggested here that Cardassia have been in occupation on Bajor for 25-30 years, yet in DS9 Gul Dukat and Major Kira both independently made reference to the occupation lasting 60 years.
The Admiral tells Picard it has been "almost 40 years" since the Cardassians annexed the Bajoran home world. Picard then says it has been "generations" since the Bajorans had a home. Since a generation is only 25-30 years, it would not really be "generations."
However, the Admiral may have been mistaken: Dukat and Kira both state that Bajor had been occupied for 60 years. That's at least two generations. Moreover, Bajoran generations may be shorter than those of humans.
When Picard and an away team beam down to talk to Orta, Picard is wearing his gray undershirt and maroon captain's jacket. After they beam back up, the team exits a turbolift onto the bridge while discussing the meeting with Picard now in his normal uniform.
After the Bajoran ship is destroyed, the admiral contacts Picard via a priority message. For some reason, Data is the one to receive the communique at the ops station. Incoming messages go through the tactical station. Even if it's possible to control communications from other stations, there's no reason it would route there first.
Gul Dolak mispronounces the name of his own species, using a long A in the second syllable (car-DAY-si-an). The proper pronunciation is car-DAH-si-an.