Wow! Impressive! I can understand most of the things that you were trying to say! Because I can't fully understand the essay, I might make some wrong or weird suggestion. So please don't hesitate to ask me or correct me. ：）

我最近看一部电视剧

可是有些演员有一个我不习惯听的口音。　→　但是有些演員的口音我還是聽不習慣，
所以对这个事情中文字幕非常实用。　→　所以中文字幕在這裡非常實用。

I don't quite understand the part below: 

虽然北京的口音应该是非常正确的中文， 有时候我还听不懂。　→　北京的口音應該是很正確的中文，但有時候我還是聽不懂。
因为很多我中国朋友来自福建省或者广东省。　→　因為我有很多中國朋友是來自福建省或廣東省。
Here do you mean that although Beijing accent should be the correct mandarin. But you sometimes don't get what you're friends, who are from 福建省或者广东省, are trying to say? 

我觉得我应该跟北京人讲话一点所以这个事情不会成为一个障碍。　→　I don't quite understand this sentence.
我跟你说， 我可能听错他们的口音， 也许不是北京的。　→　但我可能聽錯他們的口音，也許他們講的不是北京口音。