That's not a common mistake. Only one translation that I know of translates John 1.1 incorrectly as saying "the word was a god," and it is obviously done for theological reasons that cannot be justified.
ESV John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
BNT John 1:1 VEn In avrch/| beginning h=n it was o` the lo,goj word( kai. and o` the lo,goj word h=n it was pro.j with to.n the qeo,n God( kai. qeo.j God h=n it was o` the lo,goj wordÅ
The main issue is highlighted in blue. I have underlined words in the verse with articles (the - 'o' or 'tov' in Greek).... JWs argue (alone as far as I know) that since there is no article (the) attached to God (highlighted in blue), that the noun 'God' should be translated as "a god."
However, in Greek, it is quite basic that a noun can be articular without actually having an article written, and the New World Translation does not consistently translate all of the article-less nouns as anathorous (without article).
Both "God" and "word" in the second part of the sentence can be the subject of the verb - both being in the nominative case. The word order gets changed in English because usually the subject goes first in the English sentence, and since "word" has the article, it is taken as the subject, although both are articular.