On a recent commute to work, I happened to notice the words Logistic Center written in huge letters on a company building here in Germany (you can see it in one of the pictures here). As mentioned in a previous post, there are many false friends of this type that differ from the correct English word only by the letter s and are often used incorrectly by non-native speakers (for example, physics in English vs. Physik in German).
The word logistics is a particularly interesting example. First, both logistic and logistics are correct English words, but logistic is an adjective. According to Wikipedia,
Logistics is the management of the flow of resources between the point of origin and the point of consumption in order to meet some requirements […]
The expression Logistic Center is most likely a mistake related to a translation from the German word Logistikzentrum. It may also be a literal translation of the German expression Logistisches Zentrum. At any rate, the correct English expression is Logistics Center (or Logistics Centre).