Other mistake: When Bourne's 4x4 is recovered from the river, there is no damage to the rear window. But Marie was shot in the back of the head while driving away, so there should be a bullet hole. (00:20:35)
Other mistake: In the scene where Jason drops from the bridge to the boat, you see him grab his left leg/knee in pain. But throughout the rest of the film, you see him limping on his right leg.
Other mistake: When Bourne is looking up the address of Hotel Brecker on the website, the street is spelled Kurtürstendamm. It should read Kurfürstendamm with an F. The English translation of this famous street's name is "causeway of the electoral princes"
Chosen answer: They frame Bourne because Borne was actually the one who killed Neski and his wife (he was doing it on Conklin's orders). Once Pam Landy does some digging, she will realize this; then it's a simple matter of putting two and two together - the man who killed Neski would obviously have a huge motive for covering up his crime. This is why Abbot and Gretski frame Bourne: he's the perfect fall guy.