The ship that MacGyver and the girl jump off is not the same ship shown earlier. They jump from a much bigger height, as that ship is much taller.
Simply wrapping the damaged rear part of the rowboat in a tarp would not make it watertight. Also, the forward motion of the boat would cause the leading edge of the tarp to "scoop" water into the boat instead of "shedding" it, just like roof-shingles do if they're nailed on upside-down.
Mac puts the 3 satellite markers in the pipeline to alert Pete. The metal of the pipeline and then the storage tanks on the ship would completely shield the markers rendering them useless.
The rowboat that Mac pushes out into the water and rows toward the ship is solid and intact underneath the tarp, since Mac is able to push against the stern without the tarp bowing under the force of his hands, and since the boat holds water okay. This means the boat's stern was smashed out *after* the footage was shot of Mac using the boat to travel out to the ship.
The glow from the mercs' welding-torches would not have visibly moved around among the trees, because welding is done very "locally" (perfomed in a very small area on the space between the metal surfaces) in order to thoroughly heat the metal being joined, and it "proceeds" very slowly to form a proper joint.
When MacGyver rows out to the ship, a boom mic can be seen partially in the top left of the screen.
For an experienced woodsman, MacGyver doesn't wear gloves, not so much to keep his hands warm, but to protect them from the inevitable cuts and scrapes from moving through underbrush. He also sleeps in the same clothes that he wore during the day which would have made him very cold during the night.
Mac and Karin had seen the glowing lights in the forest just the previous night, and so Mac would have said, "last evening", not "the other night", when referring to when they had seen the welder's-arcs before.