When Dr. Crusher and Captain Picard are running down the hill, being chased by soldiers in the last ten minutes of the episode, you can clearly see that Gates McFadden is wearing shoes with cleats rather than the standard issue Star Fleet boots. Once the characters are on level ground again, she is wearing the regular boots again.
Beverly says the telepathic implants are connected directly to the brainstem, but Lorin says they're connected to the cerebral cortex. Given the localization of function in the human brain, an implant in the cerebral cortex would be more intuitive. The superficial location of the implants would suggest connection to the brainstem, which is a prime spot for inducing nausea. This ambiguity in neuroanatomy technobabble continues a Star Trek tradition of referring to the brain as the cerebral cortex even though it's just one (albeit large) area of the brain.
When she and Captain Picard are escaping through the cave, Dr. Crusher says she "smells gas" and then identifies the gas as methanogenic. While methane is odorless in its natural state, the "gas smell" is the result of adding an odorant so that gas can be smelled when it builds up dangerously in normal use. Since the gas in the cave is naturally occurring and we have no mention of which other components are mixed with it to become "methanogenic", there is a possibility that it COULD be smelled by Beverley. In any case, it is not possible to identify something as "methanogenic' (methane-producing) merely by smell.
As Crusher and Picard each take several steps away from each other to see if that decreases their psychic link, they both become very nauseous, but feel better when they get back together. After Crusher scans them both and finds nothing wrong, she takes only a couple steps before they get sick again.
However, the implants may have become more sensitive to the distance between the two because of the earlier separation attempt.
However, the implants may have become more sensitive to the distance between the two because of the earlier separation attempt.
When Riker goes to the quarters assigned to Mauric, he sees all kinds of equipment that Mauric has set up "for security reasons". Mauric would not be able to get the equipment onto the Enterprise, as it would have had to have been approved to be brought aboard either by transporter or a shuttle.
Picard and Crusher first meet Lorin, the security minister of the Prytt, after they are captured and isolated in a cell. Lorin does not say her name to them. Lorin later says her name to Riker. Picard then mentions Lorin's name to Crusher while they are still trapped on the planet, even though he should have no way of knowing it.
When in an escape and evade situation it is unwise in the extreme to light a campfire, as its light can be seen at a very great distance. Picard would surely know this and avoid having an open fire.