When Don and the others are looking for the Jupiter, his necklace is hung on the flap of his jacket. When the camera angle changes and he turns around, his necklace is under his shirt.
When Judy Robinson is confronting Don West (31m50s) after Don has escaped the spaceship that falls off the cliff, Don's St Christopher necklace appears and then disappears repeatedly, sometimes it's caught on his jacket's zipper, sometimes it's right against his skin, sometimes it's no where to be seen.
When Maureen is explaining the problem with the black hole, she shows the planet circling around the sun and says that the days are getting shorter. One revolution of a planet around the sun is a year. A day is one full rotation of a spinning planet. If the planet circling around the sun is the problem, they should have the equivalent of an earth year or two at least, not a few weeks unless the planet is very close to the sun in which case it would not be habitable.
Throughout the show, it is shown that liquid methane is used as fuel. The critical temperature of methane is about -83 degrees Celsius, meaning that above that temperature methane is gas independent of the pressure it is stored. It would require a cryogenic tank to store liquid methane, which the ones shown in the Jupiter ships do not resemble anything like it. Judging by the characters clothing, the ambient temperature in the planet is in +20 to +30 degrees Celsius and, therefore, methane could never be stored in liquid form.
At around 15 minutes when Angela is picking up the gun, the gun has no obvious trigger. There is the finger guard but there is no trigger.