Why is the written language inconsistent throughout One Piece?
Ashishgup mentioned general aspects of English in Japanese anime and conversely in his comment.

Beside that, note that English is an obvious feature of One Piece. The name of the manga itself is "One Piece" in Japanese, not ワンピース ! 

Looking at the Japanese version of the manga, you can quickly notice that shop signs, some brands, city signs and even some fight moves are written in English.  All important characters are introduced with their name dubbed in English in the background.

It seems then consistent that the anime keeps this feature (the anime being derived from the manga and not the other way around).

As for why it is so: mixing languages is more than ever a trend in all languages. Some mangaka will do it more than others. Eiichiro Oda does it quite a lot.