Continuity mistake: When Bourne is escaping from the Embassy, he drops the bag, which hits some metal thing on the way down, making it wobble to and fro. The camera cuts away while it's still moving and we see the marines coming upstairs. When Bourne climbs under the fire escape, we can see down to the ground and the metal thing's stopped moving. All well and good, except after the marines leave Bourne looks down, and in that shot the metal thing is moving again, then stops - obviously the rest of the shot we saw before. (00:23:46)
Audio problem: When the first assassin runs out of bullets shortly after coming through the apartment window, his gun makes a series of rapid clicks as if dry firing full-auto, but real guns, even full-auto ones, don't keep on clicking when empty. It should either make a single click, or a nearly inaudible one. (00:44:16)
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.
Factual error: After the scene where Bourne is returning to his hotel to find the police surrounding it he smashes a police car window to take a "wanted" poster from the front seat. This poster is titled "Gesucht" which is German. Requests for assistance from another police force would not simply be a matter of faxing a wanted poster to the nearest police station over the border. The request would be given to a national body who would then have translated the request to French before distribution.
Revealing mistake: When Jason climbs onto the rail of the fire escape, it is not attached to the wall - intentionally, it has not broken - but then in another shot, two seconds later, it 'breaks'. It pulls out of a visible hole in the wall, although it was never actually attached and there was no hole before. (00:23:25)
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 Jason enters the train station to stash the red bag, the large clock on the outside of the station reads exactly 12 noon. Once he's inside the station the clock reads after two. (00:48:37)
Continuity mistake: In the scene where Jason and Marie go to Jason's residence in Paris, Jason picks up a Bic Pen to write while he's talking on the phone to the hotel. He takes the cap off and places it on the back of the pen. In the next shot, the cap is missing from the back of the pen. (00:39:15)
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.
Factual error: When Conklin flies to Paris, we see him board a Dassault Falcon 900 that bears the registration "N-GIDE." This is not a valid United States aircraft registration. All US registrations have an "N" followed by up to four alphanumeric characters without a hyphen in between (e. G, N601AW). (01:35:10)
Continuity mistake: During the car chase there is a shot of Bourne steering frantically. In the centre of the steering wheel is a Mini badge. Cut back a few moments later and the badge has changed to a Cooper badge. (00:51:15 - 00:52:05)
Continuity mistake: At the beginning of the car chase, the red car has a burnt out leftside tail light. For the remainder of the chase, it's working. (00:52:57)
Character mistake: The laser pointer and the subtitle reads "Gemeinschaft Bank". That's wrong. It has to be Gemeinschaftsbank. (00:04:20)
Revealing mistake: There is no snow at all on any surface higher than the second floor of the consulate, except for the sill Bourne is climbing on, and the fire escape.
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.
Visible crew/equipment: Right at the end of the car chase, the yellow van in the pile-up is flipped over by some kind of large metal lever in the undercarriage. This is seen from the last 2 angles of the crash. (00:52:45)
Visible crew/equipment: After Bourne and Marie get to Paris, Bourne is sleeping and Marie awakens him. Shortly after he gets out of the car you can see a crew member's head reflected in the rear right window. (00:34:25)
Continuity mistake: When Bourne is escaping the embassy, he has to scale down a wall below a broken fire escape. As he is inching his way to his right, towards the corner, the shot changes to one from below, and he is suddenly about six feet lower than he was the moment before (there is a curved pipe jutting out of the wall that allows you to easily judge his actual position.) (00:23:33)
Visible crew/equipment: As Eamon is getting ready to leave with his children after Jason kills The Professor, a cameraman's legs are reflected in the back of his car just before he says the line "I'm not waiting, Marie". (01:30:35)
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.