Factual error: In the final scene with the New York skyline in the background, the new glass/stainless steel Manhattan complex at 731 Lexington Avenue is seen; this building is just being finished now in early '06. The building stands where Alexander's dept store once was. (On a related note, it is a nice touch on Spielberg's part to overlay the Twin Towers onto the skyline in that same scene.)
Factual error: The 5 German 'snipers' at the Munich airport are shown using G-3 rifles with scopes on them. None of the 5 snipers had scopes on their rifles. In fact, they didn't even have semi-automatic rifles. They used bolt rifles with iron sights. Their poor equipment contributed significantly to the failure of the rescue operation and prompted H&K to develop the PSG-1 sniper rifle.
Factual error: In the background at Avner's debriefing is a water cooler. Israel's two earliest mineral water companies (Mei Eden and Neviot) weren't founded until the 1980s, so it is unlikely that there would have been such a water cooler there (assuming that the debriefing was taking place in the mid/late 1970s).
Factual error: In the scene towards the end where Avner is speaking with his mother, there is a central-air-conditioning-type vent in the wall. It seems to me unlikely that an Israeli house/apartment in the 1970s would have had such a system. Air conditioning units were not very common and what would normally have been found was a single-piece unit installed through a wall.