Is there a trick to skinning and looting?
Unfortunately, this is an annoying part of the game. The only real 'trick' is to make sure you stand directly over the point where the animal is glowing, and you see the prompt on the screen to skin.
Same thing goes for the looting. Though, this is a much more annoying issue. The person drops the gun right next to him. You need to make sure that the game is NOT prompting you to pick up a gun, but to Loot the Body. The two points are so close, that you can jiggle between the two.
It takes practice, but I have gotten very good at this.