My big pet peeve with the German language is that there are three freaking genders (masculine, feminine, neutral). Which means you only have 1/3 chance of getting it correct when guessing.

My second pet peeve is the various different (and unrelated) meaning of the word 'ihr', which can mean in turn you (plural pronoun), her (pronoun), her (possessive determiner, as in "her book") and their (determiner). Why in the world would you reuse the same word for so many different meanings?

My favorite thing about German is that things are pronounced as they are spelled and vice-versa.