I just finished "Philosophical Investigations" and I found that Wittgenstein's writing, ironically, was difficult to understand. Perhaps this is because I am a neophyte to the discipline. I do feel he could have written better. My question is: Did Wittgenstein write in such a fashion in order to show the problems of language?

I'm not a Wittgenstein expert, but based on what I do know about his work and his life I would judge that the answer is no. Most of his published writings, including the Philosophical Investigations, were not quite written for publication in the ordinary way -- rather they consist of his posthumously published notebooks, jottings, lecture notes, etc., and may never have been intended for publication. He was the sort who was constantly grappling with philosophical questions and reflections, constantly reworking his thoughts, constantly revisiting his earlier conclusions and rethinking them -- and the writings as we read them simply reflect that fact. Yes they ARE difficult to penetrate, follow, etc., but that's more because they are deep, difficult, in progress, and unpolished, rather than because they are intentionally designed to illustrate any particular points. Personally I love reading Wittgenstein -- maybe even precisely for those reasons his writing is extremely provocative -- I sort of...