When Kate and Juliet land face-first in the mud, their clothes are already matted with mud on both sides (presumably from previous takes).
After Kate finds Jack back at "The Barracks" and Kate tells him that everyone is gone and that he was left behind, he asks "What about Julienne?" Instead of "Juliet."
The Smoke Monster tries to get at Kate and Juliet but is unable to do so, during their second encounter where they stand behind the sonic fence that kills everyone who crosses it. However, John, Sayid, Kate and Danielle are all able to climb over the fence unharmed. The monster, being a flying creature, should therefore be able to do the same thing as well, move over it. However, this assumes that the monster can fly as high as it wishes. The precise capabilities of the monster are unknown, and in fact the monster is never shown flying more than a few feet above the ground, well within the area of effect of the sonic fence.
When Juliet and Kate are hiding from the Smoke Monster, there is a little part where you see (from the monster's point-of-view) a man in a red T-shirt visible on the very left side of the screen.