The Tamarian captain, Dathon, takes the ornamentation off his uniform and places them around his campsite. The following morning Picard picks one up to examine. When Dathon runs up, however, the ornaments are back on his uniform.
Despite their apparent language barrier, the Temarians incorporate some English into their language, and the Starfleet computer is able to explain their mythology.
When the Enterprise fires on the Tamarian vessel, the phasers are fired from photon torpedo launch bays, not from the phaser banks on the saucer section. It is admitted to be a post-production mistake in the Star Trek: The Next Generation Companion. Rick Berman said the producers received hundreds of letters from fans pointing it out. This was corrected for the Blu-Ray disc release by replacing the shot with a close up of the phaser array from "The Best of Both Worlds".
As Picard shivers in the cold, watching the sleeping Captain Dathon by the campfire, a strong wind can be heard whistling and howling in the background, yet the trees, bushes, etc., all remain perfectly still.
Science and Engineering (especially that required to build and operate a star ship) require strictly clear precision, something the Tamarian language is not equipped to handle.
At the end, Riker just walks into the captain's ready room and says that he hopes he's not disturbing the captain. Protocol requires that anyone not specifically summoned should press the "doorbell" and wait for permission.
While on the planet, Picard tries to light a fire. It goes out right away, but he never tries again. Not very productive of anyone from Starfleet, let alone a Starfleet captain.