In real life, Oktoberfest does not take place in Neander Valley (north-western Germany) as claimed by the "History Kiosk", but in Munich, Bavaria (south-eastern Germany). However, the location could have changed, since 1000 years have passed.
When she first finds the chicken hat in the ship after Fry's "death", the chicken has gray wing feathers. But when she wears the hat when fighting, the chicken's wings are now white.
In contrast to the portrayal in the episode, Neanderthals were actually quite intellegent. Furthermore, DNA has shown that Neaderthals and Homo sapiens deed in fact engage in intercourse with each other.