When Picard takes the sign, "Romulans Only," he throws it letters facing down. When he walks over it, the letters are facing up.
While on the Holodeck of La Sirena, Picard suspends the program, at which points the birds stop moving midair. But the fire in the fireplace continues to flicker and burn.
The swords used in the fighting visibly bend and wobble, revealing them to be made of a soft, flexible material.
The "Romulans Only" sign is written in English using the Standard alphabet. It should be written in the Romulan language using the Romulan alphabet, especially since the purpose of the sign is to allow only "true" Romulans to attend the location.
When Raffi beams Picard up from the Romulan village on Vashti, how does she know to beam up Elnor as well? Picard is standing in a crowd of Romulan civilians. Elnor is not wearing a communicator, or any other device that would distinguish him from the other people present. And Picard doesn't tell Raffi that there is another individual with him.
The planet Vashti is said to be heavily defended against invasion, but the only countermeasures mentioned are against ships entering the atmosphere. Even when La Sirena hasn't been granted clearance to land, Picard is able to beam down to the planet's surface with no problems. In the Star Trek universe, landing on a planet is not common, but beaming down an invasion force and/or bombarding the surface from orbit are.
When berating Picard, former Senator Tenqem Adrev says that "no one asked for your help." It was previously established that the Romulan government did request the Federation's help in evacuating Romulus before its sun went supernova, which is what led Picard to attempt to assemble an evacuation fleet. In Remembrance (2020), Fleet Admiral Kirsten Clancy states that 14 member worlds threatened to leave the Federation rather than grant the Romulans' request.
Jurati tells Rios there are "over 3 billion" stars in our galaxy and "2 trillion" galaxies. The first number is too low by a factor of about 100x and the second is too high by a factor of about 10x. Current estimates are that there are between 100 billion and 400 billion stars in our galaxy, and between 100 billion and 200 billion galaxies.
Around 13:00, the background soundtrack is the prelude of Johann Sebastian Bach's Suite for Violoncello solo #, 1 G major. After the sustained high note, there should follow an ascending scale. Instead, the soundtrack starts over from measure 1 of the piece.