Revealing mistake: As Jason goes into the train to hide the bag of money, extras can be seen looking directly at him and the camera.
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.
Visible crew/equipment: When Bourne exits the car and walks to the train station to leave the bag, he is replaced by an obvious stand-in.
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.
Character mistake: The man in the morgue says in Yoruba "'I told you so, your head is not correct," not what they interpreted.
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.
Audio problem: When The Professor is driving in the BMW, you can hear the transmission engage the next gear before he is seen completing the gear change. Shortly thereafter, you hear another gear change, but The Professor's hands are nowhere near the shifter (he's reading his orders on his cellphone).
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.