Continuity mistake: After the car chase in Paris, Bourne parks Marie's car in a garage but when the cops find it later it's not the same garage. The wall in front of the car is different and the concrete column with the extinguisher is gone. (00:56:20 - 01:07:50)
Continuity mistake: When Jason is cutting Marie's hair in the hotel room, his watch is on his left wrist. When he and Marie begin to kiss, in this flipped shot Jason's watch is on his right wrist, his moles have changed sides, and the hand-held showerhead behind them is backwards as well. Next shot his watch is back on his left wrist. The flipped shot has nothing to do with the small bathroom mirror. (01:00:56)
Continuity mistake: When Wombosi is assassinated by the other agent he is shown walking down the stairs with glasses on and a turtleneck sweater. He also has another man following him. Then the next shot shows Wombosi (or a stuntman) standing in front of the window with a leather coat on and no glasses. He is obviously not walking anymore and the man behind him is nowhere to be seen. (01:03:41)
Continuity mistake: When Wombosi gets assassinated, the shot changes to a view of the sniper's scope. The glass on the window is not broken, even after a bullet was fired through it. (01:03:44)
Continuity mistake: In the scene where Jason steals a grey Ford Sierra, when Marie walks from the phone booth to the car (Jason is taping the window) she passes a red Ford Fiesta and there is a grey Renault Laguna behind it. The car they are stealing is out of shot. When they drive off their car is suddenly on the spot where the Renault was. (01:18:07)
Continuity mistake: When Bourne blows up the tank at the farmhouse, the wide shots show a solid wall of black smoke. In the closer shots there's nowhere near as much. The smoke in the first shot must be coming from the explosion, and in the closer shot we're looking right at the destroyed tank, so it can't be due to different angles. (01:26:27)
Continuity mistake: After Jason kills The Professor, we see Eamon walking to his car with his children and opening the right side passenger door. We then cut to a shot of Marie and then back to Eamon. His car's boot is now suddenly open as well as the right side passenger door, but we never hear him open it during the shot of Marie. (01:30:20)
Continuity mistake: When Jason is viewing the CIA agent from the roof of the building, Jason is standing directly behind the big letters of the name. There's a cut and you can see the agent on the bridge and in the background the building on which Jason should be standing, but Jason is NOT there. If the actor were in this clear shot, he would easily be visible. At the next cut he's back again behind the big letters. (01:36:33)
Continuity mistake: In the last firefight, after Matt Damon jumps down the stairwell, we are shown a shot at the top of the stairs where there are bullet holes in the wall. If you look carefully, you can see where they have been plastered over in previous takes. (01:47:13)
Continuity mistake: In the scene at Treadstone HQ when they are looking at the footage of Bourne and Marie in the alley, Conklin is wearing a short sleeved blue oxford dress shirt. When they zoom in on Marie to present her bio, Conklin is wearing a long sleeved shirt.
Continuity mistake: In the scene where Bourne is watching Conklin arrive on the Pont Neuf in Paris. The very first time Bourne is seen looking down at the bridge from the roof there is a long row of traffic all along its length. There is a scooter heading the direction of the traffic. Bourne gets his scope out and follows the scooter, yet from that moment on the line of traffic has magically vanished. You see the scooter through the scope about 2 seconds after you can see it on the bridge, and it would still be going along beside the traffic, but the traffic is gone.
Continuity mistake: When Wombosi is shot, the bullets come through the bottom of the window which has bars. From the outside, we are shown that the shots go into the top of the window, and there are no bars on it. There are also curtains and fabric which disappear.
Continuity mistake: In the farmhouse scene Bourne looks out a window and it is bright outside. When he looks out the glass in the door and it is dark outside. When Bourne goes outside it is bright again.
Continuity mistake: Just before the car chase, a police car pulls up behind their mini, but when they race off it's no longer there.
Continuity mistake: When Conklin is going to meet Bourne on the bridge, the people walking behind or to the side of him are constantly changing between shots.
Continuity mistake: When Jason is climbing down the side of the embassy, there is a car in the snow. When the camera cuts directly to him, then back to the aerial view, the car is gone, there are no tracks and it isn't snowing hard enough to cover the tracks.
Continuity mistake: In the scene at Treadstone HQ's where Chris Cooper is looking at the screen of the mini that Matt Damon is getting into, he takes off his glasses. It goes to the screen and then goes back to Chris Cooper and he takes off his glasses again and puts them in his breast pocket.
Continuity mistake: When Chris Cooper is going to meet Bourne on the bridge, he passes an agent in a wool cap who is facing the street. The shot changes to Bourne looking through the scope, and the man in the wool cap has instantly turned 180 degrees to face the water.
Continuity mistake: Just after Bourne knocks out Conklin and walks toward the door, his pistol is a totally black Walther P5K. When the door opens in the next shot, it has changed to a black framed pistol with a silver slide.
Continuity mistake: Throughout the movie, Marie is wearing nail polish. When Jason and her are talking in the car when he returns from the train station, however, there is a shot of her having Jason's money in her hands. She is not wearing nail polish and her fingernails are longer - someone else's hands or the scenes were shot out of sequence and she had longer nails and nailpolish.
Chosen answer: They are octopii hung up to dry in the sun. A common sight at Greek islands. If you search Google, there are pictures of them. They are humorously mentioned at http://www.thevisualrecord.com/dbphotopages/photopage.php?photo_id=80.