When Captain Picard tells Data to beam Nuria 'directly' to transporter room 1, there appears to be no logical reasoning for it. Firstly, through the whole 7 seasons, even though bridge staff operate transporters throughout, at no point before or since was it specified that they should be beamed 'directly' to the transporter room. This occasion is no more or less routine than those other times, so there is no need to specify it. Secondly, after this, he goes to the transporter room and operates the transporter himself from there, thus there is still no logic to his request to Data just moments earlier.
The Mintakans believe Picard to be a god. Liko shoots "The Picard" with an arrow to prove he is immortal. After Picard falls, Nuria reveals Picard's (red) blood on her hand to prove his mortality to Liko. The Mintakans are described as "Proto-Vulcans" which means that they have GREEN blood. Revealing that Picard's blood is red would greater add to the belief that he is a magical or mythological being.
Riker and Troi get surgically altered to look like the native people. None of the local men have any facial hair. If Riker wanted to blend in, he should have shaved or sent down someone else who was clean shaven. Not a single person he met wondered what that thing was on his chin.
Riker and Troi forget that the best way to lie is to tell the truth--just not all of it. When the Mintakans are speculating about why "the Palmer" was cast out by "the Picard", one of them could have suggested that "the Picard" sent "the Palmer" to Mintaka to accomplish a task and now awaits his return, a suggestion that would have been strengthened by the fact that two hunters have just returned after being sent by Nuria to accomplish a task (namely, getting meat).
The arrow in Liko's bow when he aims at Troi, and then shoots at Picard, has a blunt tip. This is not the type of arrow to use when attempting to kill any animal the size of a human. It would hurt, but it is doubtful that it would penetrate.
The goof item below may give away important plot points.
When Dr. Warren dies in Sickbay and Picard and Nuria are standing over her body, Dr. Warren's hand (which was left resting on her chest) can be seen at the bottom right of the frame rising and lowering as the "dead" doctor breathes.