Continuity mistake: Early in the film, Matt Damon is running up several flights of stairs. He is shown walking around a corner when the camera suddenly cuts to a different angle. In the new angle, he is shown running around the same corner. (00:22:27)
Continuity mistake: During the car chase in Paris, the sun shines when the camera films the front of the car Bourne is driving, but it's grey and gloomy when the camera films the rear of the car. Changes back and forth throughout the entire car chase.
Continuity mistake: In the car chase scene, the windscreen wipers on the Mini change from being on, then to off, then back on again throughout the whole chase. (00:52:42)
Continuity mistake: After Bourne dyes and cuts Marie's hair, she is left with long tendrils at her temples. He brushes them away when they start kissing. But the next morning, when Marie wakes up in bed, all of the front of her hair is cut short.
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 Bourne first wrestles with the boat's doctor/captain, the man shows Jason the cylinder that was in his hip and asks him why it was there. Jason grabs it and his hands are clean, then in the next shot as the medic is still holding him there is blood all over Jason's hand as Jason continues examining this cylinder, then the blood disappears again.
Continuity mistake: When Jason breaks through the embassy fire escape door onto the outside platform the metal door has two round keyholes. However, when he climbs up onto the railings it's a different door which has a different type of lock with a rectangular keyhole cover plate. Also, initially there is a chain welded to the top of the left hand railing above a small hinge and extending across to the right-hand railing. The next shot shows the chain wrapped around a large hinge further down on the left-hand railing. (00:23:07)
Continuity mistake: When Jason is on the 5th floor of the embassy looking for an exit he is holding a walkie-talkie in his right hand, wearing white earphones and carrying the red bag on his left shoulder. In the next shot the white earphones and walkie-talkie have disappeared and the red bag is suddenly on his left shoulder. The bullet hole pattern in Jason's back has also been reversed as if the scene had been flipped. (00:22:32)
Continuity mistake: When Bourne sees Conklin on the bridge of Pont Neuf, Conklin starts to take his jacket off first, leaving his suit coat on. In the next shot both jacket and coat are being taken off at the same time.
Continuity mistake: When Jason and Marie are talking before she gets in Eamon's car, one angle shows light snowfall and snow in Marie's hair. But the other angle, there is no snow in her hair, even when she fully turns around to get in the vehicle.
Continuity mistake: When Jason jumps down the staircase hole, the position which he lands in and the amount of blood on his head changes between shots.
Continuity mistake: In the Paris Gare du Nord shot where he is to leave the bag, when they pull up to the station time is 16:15 in the first shot of the watch, then cut to car he gets out, time is 12:00 then inside time table show around 16:30 unable to see how long up, but it is no longer 12:00 then camera moves around him and cut and a time table for track 12 shows 18:26 He looks at the timetable pondering if he should leave Marie and now the timetable for track 12 shows 14:37 and the clock in the background 14:29.
Continuity mistake: As Bourne is running through the embassy, the red bank bag alternates multiple times between being over his right shoulder and his left.
Continuity mistake: During the car chase in Paris a cop's motorbike crashes against a car and he flips over it, flying meters away. A frame later he is simply landing a couple centimeters next to the car.
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.