A typical problem when translating English to German is how to deal with English tenses. English is nitpickingly accurate about sequence and duration of events, while German is extremely sloppy.
Another thing to worry about is direct/indirect vs. Dativ/Akkusativ/Genitiv objects. English uses prepositions in much more occassions than German because of that and English speakers may try that in German too. Oh, and of course, prepositions cannot be translated 1:1. That's a problem in both directions.
A very hard problem when translating German to English (or nearly any other language) is how to transport the meaning of modal particles. There are plenty of these words, and they change the mood of the sentence. One has to insert additional explanations into English, which is often lengthy and awkward.