When the Kzinti captain changes the weapon from laser to telescope, the animation sequence is out of order; he's holding the laser, holds up the telescope, changes it into the laser, and is then holding the telescope.
The Kzinti captain changes the Slaver weapon from telescope to laser. When he raises his arm to aim at his captives, he holds the telescope, but in a following shot, he holds a laser.
When the shuttle opens, the doors slide left and right, but this is clearly impossible because there is neither a track nor slots for them to slide into.
At 16:45 especially, the life support glow surrounding Spock and Sulu is a little off the mark.
One of the weapon's settings neutralizes all the power in the area - except, conveniently, the Starfleet life-support belts and the Kzinti spacesuits.
The shuttlecraft's sensors would have detected the Kzinti and their ship before landing. Spock would have also detected them with his tricorder.
Spock seems surprised that the weapon includes an "energy absorber," yet he later states that the weapon has, so far, shown no technology beyond anything the Federation already has.