Hi Jesusfreak,
I don't ever remember Jesus being taught as the mediator for all Christians by JW's.
Here is a quote I found:
*** w89 12/15 30 Do You Remember? *** • In what sense does Paul use the term “mediator” when referring to Jesus at 1 Timothy 2:5, 6? In this text, Paul uses the Greek word me·si'tes for “mediator,” which term has a legal significance, so he is not using this word in the broad sense common in many languages. Hence, Paul is not saying that Jesus is Mediator between God and all mankind. Rather, he is referring to Christ as legal Mediator of the new covenant, which laid the basis for Christ’s anointed followers to share with him in his heavenly Kingdom. (2 Corinthians 5:1, 5; Ephesians 1:13, 14; Hebrews 8:7-13)—8/15, pages 30, 31.
You can read more Watchtower quotes about this here: http://www.jwfiles.com/mediator.htm
Only those in their "heavenly / anointed" class are considered to have Jesus as their mediator. The vast majority, 99.8% of JW's, are considered the "earthly" class and do not have Jesus as their mediator. These are the ones who also are prohibited from taking the wine and the bread at their annual Memorial of Jesus' Death, coming this Saturday to a Kingdom Hall near you.