The current interpretation of the Watchtower Society is that Christ’s role as mediator applies only to a small group of individuals - the 144,000. The assumption is that since the new covenant applies to their roles and kings and priests, Jesus’ mediates between them and Jehovah God, while those with an earthly hope are often described as ‘beneficiaries’ of this arrangement. For more information on this, see jwfacts.com
There is some shifty reasoning used by the Society to justify their view that Christ actually mediates for fewer people than Moses:
The Watchtower of November 15, 1979, page 26, made this comment:
“What, then, is Christ’s role in this program of salvation? Paul proceeds to say: “There is one God, and one mediator between God and men [not, all men], a man Christ Jesus, who gave himself a corresponding ransom for all.”—1 Tim. 2:5, 6.
The insertion "[not, all men]" is the Society blatantly changing the meaning of the Bible.
This question was raised again in a 1989 Questions From Readers (w 8/15/89 p 30-31):
“Is Jesus the Mediator only for spirit-anointed Christians or for all mankind, since 1 Timothy 2:5, 6 speaks of him as the “mediator” who “gave himself a corresponding ransom for all”?”
The Watchtower answer to this question on the mediator centers on the following legal concept:
“The Greek word me·si′tes, used for “mediator,” means ‘one who finds himself between two bodies or parties.’ It was a ‘many-sided technical term of Hellenistic legal language.’ Professor Albrecht Oepke (Theological Dictionary of the New Testament) says that me·si′tes was “one of the most varied technical terms in the vocabulary of Hellen[istic] law. ” (w 8/15/89 p 30-31)
So, it is a "many-sided technical" term. But they never bother to define what it means! Nor do they cite the source.
However, after some searching you'll find comment was taken from the 1967 edition of the Theological Dictionary of the New Testament. Notice what this dictionary stated on page 588 (1985 edition) regarding 1 Timothy 2:5, 6:
“In 1 Tim. 2:5-6 we find a Christianized use. The one God wills that all people be saved, and there is one Mediator representing God to them and them to God, i.e., Christ Jesus in his sacrificial death.”
Beginning to see a difference in how mediator should be defined?
Professor Jerome H. Neyrey, Ph.D. (Yale University), a professor of New Testament Studies at the University of Notre Dame, made the following comments on Oepke’s definition:
Writing on "mediator" in 1967, Albert Oepke identified the following social roles in the ancient world that exemplify the role of broker or mediator. A mesites is a person who (I) is "neutral" to two parties and negotiates peace or guarantees agreements, (2) arranges business deals, (3) receives as king divine laws and offers sacrifice for the people, (4) offers as priest prayers and sacrifice to God on behalf of individuals and the people, (5) brings as prophet a teaching or mighty work from God, (6) founds a new cult or religion, and (7) delivers as angel communication from God.
As Oepke also notes, the New Testament calls Jesus a broker in many ways: he is the unique mediator between the one God and humankind (1 Tim 2:5), the mediator of the new covenant (Heb 8:6; 9:15; 12:24) and a "priest according to the order of Melchizedek" (Heb 5:6; 6:20; 7:17). In contrast to the Levitical priesthood, Jesus' priesthood/brokerage is vastly superior because Jesus "is able for all time to save those who draw near to God through him, since he always lives to make intercession for them" (Heb 7:25). - Worship in the fourth gospel: a cultural interpretation of John 14-17 -- Part II
Finally, to put this legal word business to rest, here is how should we legally define the word mediator as used by Paul:
“[Paul] calls him the mediator, the mesities. Mesities comes from mesos, which, in this case, means in the middle. A mesities is, therefore, one who stands in the middle between two people and brings them together. When Job is desperately anxious that somehow he should be able to put his case to God, he cries out hopelessly: 'There is no umpire [mesities] between us' (Job 9:33). Paul calls Moses the mesities (Galations 3;19) in that he was the one between, who brought the law from God to the people. In Athens in classical times, there was a body of men - all citizens in their sixtieth year - who could be called upon to act as mediators when there was a dispute between two citizens, and their first duty was to bring about a reconciliation. In Rome, there were arbitri. The judge settled points of law; but the arbitri settled matters of what was fair and just; and it was their duty to bring disputes to an end. Further, in legal Greek, a mesities was a sponsor, a guarantor or a surety. He put up a bail for a friend who was on trial; he guaranteed a debt or an overdraft. The mesities was someone who was willing to pay a friend's debt to make things right again.”
- William Barclay (1907-1978), Professor of Divinity and Biblical Criticism Glasgow University in Scotland, Letter to the Hebrews, p. 106.
Biblically speaking, Jesus ‘bailed out’ all that faithfully accept his ransom sacrifice. He paid our debt, the debt incurred by sin, with his shed blood. This cannot possibly be applied to a limited group of individuals. Paul’s use of this legal term (when the actual definition is understood) is all-encompassing and should not be limited to a certain elite class of people.
The only reason for maintaing this teaching is so the Governing Body can enforce their claim of authority as the mediator appointed over Christ's belongings that all must support in order to 'be saved'.