I just stumbled across a post from last year on the Guardian's language learning blog. It's by a guy trying to learn Spanish using only Duolingo, and I thought his feedback was quite interesting.
The author Alan Haburchak, found himself struggling to internalise the grammar of Spanish as there is no conscious presentation of verb tables. I found similar problems using the course for German -- not with the verbs (I'd done most of the verb system via the Michel Thomas course already), but with the articles. The declension of the articles in German is more complex than verb conjugation, because there are so many sets of overlaps. There is no marking for gender for plural, but gender is marked in singular. The feminine declension matches the plural declension in 3 out of 4 cases. Masculine and neuter declensions match in genitive and dative, but not nominative and accusative... and the neuter nominative and accusative are the same as each other, but not the masculine ones. I'll stop now because I've probably lost you, and that's only half of it. And when you've finished with the definite articles, there's the indefinite ones too, and the adjective endings which are more complicated again. Certain patterns are shared, certain are distinct.
Trying to learn such a complex and arbitrary pattern from examples is, I think, pretty much impossible. So much information is obscured (not least of all the gender of the noun) that you cannot generalise. The end result is an ability to read fairly comfortably, but not to reproduce.
Since I started looking at tables myself, I've found the German course much easier, but still not trivial. Alan's doubt was about whether this was a general problem with "naturalistic" learning, or just his own habits formed through school language classes. I could (and maybe should) have the same doubt, but I just cannot fathom how anyone would intuit these patterns without some conscious knowledge to help them sort through the tangle.