As a native English speaker (well perhaps not entirely native, I was born in Russia and immigrated to the U.S. at the tender age of 7) I would have to say that apart from the obviously difficult aspects of the English language such as tenses, an unorthodox phonetic system employed in the language and infuriating exceptions for just about every single rule, the two most puzzling features are the Verb+Participle+Preposition combinations and the sheer vastness of the vocabulary. Observe the former...
come+up+with
come+down+with
come+foward+with
come+out+for
come+down+to
Five different constructions which would be clear as day to any native speaker, are nevertheless mind-boggling to someone who is learning the language. Notice how they all start with "come", and then imagine that sort of illogical word-scrambling applied to every verb. Daunting, isn't it? Don't know how to break it to you folks, but I haven't even scratched the surface.
Now as to the latter, I am more than happy to have dictionary.com present proof of this phenomenon in my stead. Let's take a look at the word "jump". I mean, how many possible synonyms could there be for this word? Well, one simple search can help us find out. Here's the link:
http://thesaurus.reference.com/browse/jump
40 entries for the first definition alone. FORTY. Forty different ways to say jump. But when you break it down, do all 40 words have the same meaning? Of course not! Nosedive means to jump into something headfirst, as in a pool of water or (if you're very unfortunate) onto a hardwood floor. To spring is to jump up energetically, with an almost almighty "lurch" (another word for jump right there :P) whereas to "bob" means to make jumping motions without every actually taking your feet off the ground. The list goes on and on. No other language I'm familiar with has such variety when it comes to synonyms, be it for seemingly uncomplicated actions or deep philosophical concepts.
Although English is my native language, I am also a nearly native speaker of Russian (I give credit to my parents for preserving the language of the "motherland" and passing it on to me) and fluent in German. I find Russian to be an incredibly expressive language with just as many (if not more) nuances as English, and its ability to convey feelings of dislike, anger or downright hateful fervor (i.e. swearing) is, in my experience, unmatched. German is an incredibly logical language, and once grammar constructs are mastered, relatively straightforward in its application. Mastering German grammar is a challenge however, and word order is an utter nuisance in some situations.
Just my two cents.