The idea of a unknown son in danger is good and provides good scenes for Picard but it needs more refinement to increase the tension and make it plausible.
If DaiMon Bok wants to kill Picard's son, why warn Picard? Perhaps because Bok hasn't been able to locate the son. Searching for and then running to grab that son does the job that Bok perhaps wasn't able to do. This obvious risk is not even mentioned before the Enterprise dashes off to rescue him. It should be mentioned as a risk.
There is a moderately interesting puzzle as to how Bok is contacting them. It is incredibly foolish for Bok to use a secret transport method to talk to Picard when normal communication would do. Repeating any covert action increases the chance of discovery, so us it sparingly. Bok's objective is to cause Picard fear and pain, so far more effective would be to transport threats. Have a jug of juice and ornate glasses appear in both the captain's and son's room. Spike them with a sedative. Picard sees the jug as out of place and immediately calls to his son, who does not answer, they rush to his room and find him unconscious. Bok then calls them a needles Picard about how it felt when he thought his son might die and then boasts about being able to reach out and kill him at any time.
Alternatively, since Picard is a history buff, Bok could transport historical objects used for killing or punishment. Since Picard is French, leave the blade of a guillotine on his desk and show how vulnerable the son is by appearing in the son's room and locking him into a guillotine that is missing the blade. Surely that would drive up the tension far more effectively.
Ideally, it would be a series of threats that gradually increase. The enterprise detects the transport method but cannot detect the source because it is only used to beam objects to the enterprise. Later, when Bok beams the son off the Enterprise, then they can follow it to locate the destination and send Picard there.
The standoff on Bok's ship was disappointing. In any real world, since it takes time for a transported person to appear, they would stun any intruder on sight. Bok would tie up the unconscious Picard and wait for him to awake, gleeful that Picard is there to watch his son's death. Then Picard, from a position of weakness, can expertly talk his way out of a no-win situation, convincing Bok's accomplices to subdue Bok. (ex. He's not a DaiMon, the Ferengi authorities have been notified and are on their way to bring Bok back to prison, the Enterprise now knows how to track this ship and will arrive within 10 minutes, there is no escape, etc.)
Why have the revelation that he is not Picard's biological son? That's not needed to deflate Bok. If the writers want to run with that, then there should be foreshadowing. During Beverly's medical exam, she could discover an implant, broken bone, a scar, or something that the son didn't know that he had, and he could recant a story of some weekend when he blacked out and lost track of time (the time needed to change his DNA). After Picard's hair joke, he could say that his hair has already started to recede and that it started after that blackout incident (perhaps not explicitly but both being stated as "one year ago." Bread crumbs for attentive viewers to follow.
If a true son, then Bok could be headed to a Federation prison where he cannot bribe the guards. Or otherwise explain how Bok will not be able to repeat the attempt.
Other annoyances: How can the transporter get an adequate lock on a person that the sensors cannot fully identify? Doesn't make sense, so skip it. Also, skip the "He's in danger just when we arrived." What a miraculous coincidence. Laughable. Just find him and transport him.
Why is there a Federation planet that lacks food?
If DaiMon Bok wants to kill Picard's son, why warn Picard? Perhaps because Bok hasn't been able to locate the son. Searching for and then running to grab that son does the job that Bok perhaps wasn't able to do. This obvious risk is not even mentioned before the Enterprise dashes off to rescue him. It should be mentioned as a risk.
There is a moderately interesting puzzle as to how Bok is contacting them. It is incredibly foolish for Bok to use a secret transport method to talk to Picard when normal communication would do. Repeating any covert action increases the chance of discovery, so us it sparingly. Bok's objective is to cause Picard fear and pain, so far more effective would be to transport threats. Have a jug of juice and ornate glasses appear in both the captain's and son's room. Spike them with a sedative. Picard sees the jug as out of place and immediately calls to his son, who does not answer, they rush to his room and find him unconscious. Bok then calls them a needles Picard about how it felt when he thought his son might die and then boasts about being able to reach out and kill him at any time.
Alternatively, since Picard is a history buff, Bok could transport historical objects used for killing or punishment. Since Picard is French, leave the blade of a guillotine on his desk and show how vulnerable the son is by appearing in the son's room and locking him into a guillotine that is missing the blade. Surely that would drive up the tension far more effectively.
Ideally, it would be a series of threats that gradually increase. The enterprise detects the transport method but cannot detect the source because it is only used to beam objects to the enterprise. Later, when Bok beams the son off the Enterprise, then they can follow it to locate the destination and send Picard there.
The standoff on Bok's ship was disappointing. In any real world, since it takes time for a transported person to appear, they would stun any intruder on sight. Bok would tie up the unconscious Picard and wait for him to awake, gleeful that Picard is there to watch his son's death. Then Picard, from a position of weakness, can expertly talk his way out of a no-win situation, convincing Bok's accomplices to subdue Bok. (ex. He's not a DaiMon, the Ferengi authorities have been notified and are on their way to bring Bok back to prison, the Enterprise now knows how to track this ship and will arrive within 10 minutes, there is no escape, etc.)
Why have the revelation that he is not Picard's biological son? That's not needed to deflate Bok. If the writers want to run with that, then there should be foreshadowing. During Beverly's medical exam, she could discover an implant, broken bone, a scar, or something that the son didn't know that he had, and he could recant a story of some weekend when he blacked out and lost track of time (the time needed to change his DNA). After Picard's hair joke, he could say that his hair has already started to recede and that it started after that blackout incident (perhaps not explicitly but both being stated as "one year ago." Bread crumbs for attentive viewers to follow.
If a true son, then Bok could be headed to a Federation prison where he cannot bribe the guards. Or otherwise explain how Bok will not be able to repeat the attempt.
Other annoyances: How can the transporter get an adequate lock on a person that the sensors cannot fully identify? Doesn't make sense, so skip it. Also, skip the "He's in danger just when we arrived." What a miraculous coincidence. Laughable. Just find him and transport him.
Why is there a Federation planet that lacks food?