(Recasts first paragraph, adds new comment, updates prices) * US private payrolls weaker than forecast, dollar slips * US services sector index falls in September, factory orders rise * BOJ money market data shows no intervention on Tuesday By Gertrude Chavez-Dreyfuss NEW YORK, Oct 4 (Reuters) – The dollar fell on Wednesday, tracking the pullback in U.S. Treasury yields, amid a mixed set of data suggesting that there are pockets of weakness in the world’s largest economy, further diminishing the odds of another interest rate hike by the Federal Reserve before the end of the year. The yen, on the other hand, was slightly firmer against the greenback, moving away from the closely watched 150-per dollar mark, as a short-lived surge in the previous session stoked speculation that Japanese authorities may have intervened to support the currency. The dollar index, which tracks the greenback against six peers, was down 0.3% at 106.69, giving up some of its recent gains, after weaker-than-expected U.S. private payrolls based on the ADP National Employment Report. The index, however, remained within striking distance of a nearly 11-month high of 107.34 reached in the previous session. The dollar did retrace some of its losses after U.S. factory orders gained 1.2% in August, compared with expectations of a 0.2% rise. That more than offset the moderate decline in a U.S. services sector index last month. “This morning’s services sector data helped soften expectations ahead of…