I have helped some people on here with their Dutch. One of the most frequent mistakes is a wrong word order in sentences. It is fairly simular to English, so you'll have less of a problem with it. The most made grammar mistake made by Dutch speaking people is the so called t-rule. It even has it owns wiki entry in Englsih: http://en.wikipedia.org/wiki/T-rules

I agree with Alexander that word order is the most important grammar to learn in Dutch, especially the position of the verbs. Here is the most important rule for beginners: The verb that changes with the subject (finite verb) ALWAYS goes to the second place in the sentence (the first place is usually for the subject). All other verbs (infinitives, participles) go to the end. Good luck!