Well, the Jehovah's Witnesses use as their Bible the corrupt New World Translation .  In this translation John 1:1 says that "the Word became a   g od ", instead of as in the King James Bible "the Word was G od ".  

King James Version (KJV) Bible translation:
John 1:1
1 In the beginning was the Word, and the Word was with God, and the Word was G od. (KJV)

New World Translation (NWT) 'Bible' translation:
John 1:1-51
1 In [the] beginning the Word was, and the Word was with God, and the Word was a g od. (NWT)  

     Likewise with your above mentioned Scripture (Psms 82:6) wherein the Jehovah's Witnesses Bible quotes it as "man has the potential to become a "g od", " the King James says "Ye are g ods ".   There is a difference.  The word used here for "god" is elohiym which in another place (Psm 8:5) is translated to "angels"   

Ps 8:4-5
4 What is man, that thou art mindful of him? and the son of man, that thou visitest him?
5 For thou hast made him a little lower than the angels  [elohiym] , and hast crowned him with glory and honour.  (KJV)

Ps 82:6
6 I have said, Ye are gods  [elohiym] ; and all of you are children of the most High.  (KJV)

gods : Hebrew word #430  'elohiym (el-o-heem'); plural of 433; gods in the ordinary sense; but specifically used (in the plural thus, especially with the article ) of the supreme God; occasionally applied by way of deference to magistrates; and sometimes as a superlative: KJV-- angels , X exceeding, God (gods)- dess , -ly), X (very) great, judges , X mighty.

     Below are other places that illustrate thatthe Hebrew word elohiym (God or god) is not always speaking of the One true God Yehovah (YHVH):

Exod 22:28
28 Thou shalt not revile the gods  [elohiym] , nor curse the ruler of thy people. (KJV)

Ps 82:1
1 God standeth in the congregation of the mighty; he judgeth among the gods  [elohiym].  (KJV)
Gen 30:8
8 And Rachel said, With great  [elohiym] wrestlings have I wrestled with my sister, and I have prevailed: and she called his name Naphtali. (KJV)

Gen 31:30
30 And now, though thou wouldest needs be gone, because thou sore longedst after thy father's house, yet wherefore hast thou stolen my gods ? [elohiym]  (KJV)

Exod 12:12
12 For I will pass through the land of Egypt this night, and will smite all the firstborn in the land of Egypt, both man and beast; and against all the gods   [elohiym] of Egypt I will execute judgment: I am the LORD  [Yehovah ] . (KJV)

Exod 20:23
23 Ye shall not make with me gods  [elohiym]  of silver, neither shall ye make unto you gods  [elohiym]  of gold. (KJV)

Exod 22:8
8 If the thief be not found, then the master of the house shall be brought unto the judges  [elohiym] , to see whether he have put his hand unto his neighbour's goods. (KJV)

Exod 22:20
20 He that sacrificeth unto any god  [elohiym] , save unto the LORD  [Yehovah ]  only, he shall be utterly destroyed. (KJV)

IKing 11:5
5 For Solomon went after Ashtoreth the goddess  [elohiym]  of the Zidonians, and after Milcom the abomination of the Ammonites. (KJV)

Now getting back to our Scripture in question, i.e.,

Ps 82:6
6 I have said, Ye are gods; and all of you are children of the most High.  (KJV)

We see Jesus explain this Old Testament Scripture; going to the New Testament:

John 10:34-35
34 Jesus answered them, Is it not written in your law, I said, Ye are gods?
35 If he called them gods  [no article] , unto whom the word of God [has the article] came, and the scripture cannot be broken;  (KJV)

     Jesus uses the Greek article (the) with the second word "God" in the Scripture showing that when He said that we were ‘gods" that were not the same as THE God. The Strong's dictionary brings forth the importance of the Greek article, observe:

God : Greek word #2316  theos (theh'-os); of uncertain affinity; a deity, especially (with NT:3588) the supreme Divinity; figuratively, a magistrate; by Hebraism, very:KJV -  exceeding, God, god [-ly, -ward].

The Greek word (New Testament) #3588 is the article which does not always appear in the English translation but is so very important in the Greek. 

(The definite article) : Greek word #3588  ho (ho); including the feminine he (hay); and the neuter to (to); in all their inflections; the def. article; the (sometimes to be supplied, at others omitted, in English idiom ): KJV - the, this, that, one, he, she, it, etc.

PS: Unlike the English, the Greek has no such thing as an IN definite article (a, an); so don't let the term "definite article" confuse you in that regard; the ‘article' in the Greek IS ALWAYS the ‘definite article' (the, that, this)?they are one in the same.

In the English the indefinite article is rendered as: "god" (a god).
              "           definite article is rendered as: "G od" (The G od).

So that in the Greek, the lack of an article CONSTITUTES an indefinite article statement.  Observe:

In the Greek the 'indefinite article idea' is rendered as: " theos " (a g od).
              "           definite article is rendered as: " ho Theos " (The G od).

Many (most) times the 'article' is exhibited in the English language as a capitalization of the word, in the Greek New Testament Manuscripts there are no capital letters in the Greek regarding the indication of the article, the manuscripts are all in the same case (upper or lower) depending on the age of the manuscripts (In fact, one classification of the GREEK Bible manuscripts are called the "unicals" because they are all in uppercase letters; so thus is the method and need for the Greek article to show emphasis and to set aside certain words and ideas.)

     So an analogy in our modern day English would be that if I write of a "husband" in general I would write it in English as "husband."  But if I were referring to a specific woman's husband, I might illustrate that by placing it in capitalization, or also by placing a demonstrative before it.  Observe:

"Many husbands love their wives, but Sally loves only her husband.  The men, the h usbands of the Church Board, asked Mary, "Where is your beloved, your H usband?"

     In the above, in English, I relayed the fact that this particular man, this Husband of Mary's, was apart from all other husbands on the earth, by using the word "her " and "your" before the word husband .  Well, the Greek language has different rules, in the Greek the above paragraph might look something like this transliterated:

"Many husband love wive, but Sally love the [article] husband.  men, husband church board asked Mary, "Where beloved, the [article] Husband?"

     Ya know what I am trying to say?  I hope that helps.