In the last minutes, where they are re-approaching the Lantree, the crew member behind Worf (left of him from the viewer's standpoint, at the computer station) changes several times. In close-up shots, it's a person wearing a red shirt, but in wide shots of the bridge, it's someone wearing a blue shirt.
Rapid aging should not affect hair color except at the root where the follicle is still living.
Both the research station and the USS Lantree have been exposed to the infection.
It is curious that the crew on the USS Lantree died prior to the crew of the research station. All the people on the research station would be dead as well.
In actuality, once the transporter was able to cure Pulaski of the rapid aging disease, she should have stepped off the transporter pad as an old and naturally aging woman instead of being restored to her youthful self.
Data arrives at Darwin Station but returns via transporter, abandoning the shuttle craft at the station. It's "abandoned" because, for all they knew, the shuttle craft had been contaminated.
The doctor on the station guides Data and Dr. Pulaski up the stairs to see the children. As she raises her right hand to gesture them up the steps, it looks as if what can be seen is where her 'old woman' makeup ends and her real skin begins, but watching the end of the subsequent scene on the station (around the 33:50 mark), it is seen when she raises her hand to her face that she is merely wearing latex gloves. This would not be unusual for a doctor.
Data identifies the USS Lantree captain as L.I. Telaka. Seconds later, when Picard takes over command of the Lantree, he uses the name Isao as the captain's name. However 'Isoa' could be from the initial 'I', representing his middle name. It is not uncommon for people to use their middle name as a given name, as with James *Paul* McCartney, the Beatles' bass guitarist..
When the Enterprise intercepts the USS Lantree, they remote-access the ship's functions, but they do not remote-pilot the shuttlecraft.
When Data walks into shuttle bay 3 to assist Dr. Pulaski the door is incorrectly labeled as "Holographic Environment Simulator 2" AKA Holodeck 2.
As see in Coming of Age (1988), in this episode, and in a number of others, the exterior visual of a shuttlecraft leaving the Enterprise is not properly matched to the orientation of the ship, making the shuttlecraft seems to slide sideways rather than making a proper turn.
The research facility uses cathode-ray tubes.
The Darwin Station crew are experimenting with genetic engineering, which violates Federation laws that were enacted due to the lesson of the Eugenics Wars. This issue is a recurring theme in Trek, yet is never once addressed in this case.
Although the Star Trek: Strange New Worlds (2022) episode Ad Astra Per Aspera (2023) might give a possible explanation for this. In the episode, it is said that the law that forbids genetic manipulation within Starfleet is going to be altered to allow genetically altered species to exist within the federation. It is very well possible that the law was further lifted by the 24th century to allow for genetic manipulation when certain conditions are met.
Although the Star Trek: Strange New Worlds (2022) episode Ad Astra Per Aspera (2023) might give a possible explanation for this. In the episode, it is said that the law that forbids genetic manipulation within Starfleet is going to be altered to allow genetically altered species to exist within the federation. It is very well possible that the law was further lifted by the 24th century to allow for genetic manipulation when certain conditions are met.
The events show that the transporter is a Fountain Of Youth, and now everyone in the Federation and beyond can remain eternally young. All you have to do is save a strand of your young DNA when you are twenty years old or so. On your eightieth birthday, assuming you make it to that age, just take this DNA sample, put it in the transporter buffer, run yourself through the transporter, and viola! You can once again be your youthful self, assuming that this process also keeps your memories intact when you were your old self. Not only does the transporter have the ability to do all of those things, it can also smooth over wrinkled skin, restore hair color, and eradicate bad hairdos.
Curing the people is not sufficient. They must decontaminate the research station to eliminate the children's antibodies that are floating around as well. Since they can decontaminate the research station, then they could decontaminate the Lantree as well, after beaming off all of the bodies.
Dr. Pulaski tells Picard that she has to "breathe the same air" as the child she needs to examine in order to do it right. She could have easily worn protective head gear to avoid breathing the same air as the child in order to avoid any possible transmission of a disease from him. She gives no rationale for her having to breathe the same air as the subject.