I think this depends somewhat on the language. For some, grammar is the first major bottleneck to get to a usable beginner level, but for others, it's pronunciation. For example, Danish grammar is relatively simple (which is one reason Google Translate is very good translating it), but it's quite difficult for non-native speakers to pronounce it intelligibly. I've also heard second-hand that pronunciation is a bigger problem than grammar for beginning Mandarin Chinese speakers.
It turns out that the obstacles are the same for both: tonal inflection. Most people are familiar with this fact as it pertains to Chinese and many of the languages of southeast Asia (Thai, Vietnamese, Cantonese et al) but remain completely unaware that it also a core feature of the languages of Scandinavia, Danish included. btw, Google translate does an excellent job translating Chinese (but a pretty terrible job with a superficially related language like Japanese). It turns out Chinese and English word order are the same.
I think this depends somewhat on the language. For some, grammar is the first major bottleneck to get to a usable beginner level, but for others, it's pronunciation. For example, Danish grammar is relatively simple (which is one reason Google Translate is very good translating it), but it's quite difficult for non-native speakers to pronounce it intelligibly. I've also heard second-hand that pronunciation is a bigger problem than grammar for beginning Mandarin Chinese speakers.