Coryn is absolutely right. Any sort of speech pattern, whether it be an accent or an impediment is irritating when it's brought up over and over again. In the case of an accent, make sure that the reader knows the character has an accent, and reinforce it here and there, but you don't need to write things as they sound. Just make sure the reader knows that they have an accent, and they can imagine it themselves. Gotta have faith in the reader's imagination. You can, however, put in little changes in dialect, like an Australian person saying 'mate' or a Canadian saying 'eh', just don't overdo it.
As for impediments, which you didn't ask about but I'm going to bring up anyway because it's just as irritating when done wrong, it's pretty much the same. You see stutters and lisps in writing all the time, and you absolutely do not want to write every word the character says in broken or lisped English (or whatever language you're writing in). Not only is it hell to read, but it looks unprofessional, in my opinion.
TLDR speech patterns are a great way to give a character more of an identity or depth, but you've gotta make sure you don't make it annoying or difficult to read, or you could have the opposite effect you want on the reader. Just my two cents.