The main problem is that it doesn't provide context information. It just lists a bunch of translations without telling you when they're appropriate. As for lexical errors: I don't have statistics but it seems to me that the English-Spanish dictionary currently works best. (But this may just as well be an artifact of my limited command of Spanish)
To be fair on the duolingo team, it might be very hard to provide context-appropriate translations and that's why they need us.. but it's surprising and a little disappointing to learn that they would provide a translation that would never be right in any context (I'll report it).. I'm (selfishly) glad to know you don't think the English-Spanish dictionary is as problematic, maybe partly because there are many native Spanish speakers on the team? And maybe the English-German dictionary is particularly problematic because of the compound words?
Making the software automatically fit contexts would be very hard indeed. They'd have to solve the AI problem for that ;-) What they could (and should) do is licensing an external dictionary like pons to not just provide a bag of words but also context information. It'd still be your job to decide which context applies to a specific situation. As they neither have the expertise nor the manpower to build a good dictionary on their own, I think licensing is the most viable option.
This http://is.gd/oqlRIa is much more useful than just listing 'transmission ratio, translation, rendition' as possible translations of 'Übersetzung'.
Is it just me or are other users of this app having a hard time understanding the female speaker? I use the Memrise app and I have no difficulty understanding the voices they use. Memrise even has native German speakers that I can understand better than the female speaker with this app.