According to UN Watch:
"UN committees, annual UN resolutions, an entire UN bureaucratic division, permanent UN exhibits in New York and Geneva headquarters -- all dedicated to a relentless and virulent propaganda war against the Jewish state. Together, they have made the UN into Ground Zero for today's new anti-Semitism, which is the irrational scapegoating of Israel with the true intended target being Jews. Not only do these anti-Israel measures incite hatred against Israelis and Jews everywhere, but they have done not a thing to help the Palestinian situation. On the contrary: they give strength and succor to extremists.
Paradoxically, one of the greatest violators of the UN Charter's equality guarantee has been the UN body charged with establishing and enforcing international human rights, the Human Rights Council."
There's one widespread image in pro-Israel sites depicting bias in UN though I couldn't find link to Sun News video where this image was taken from:
And speaking about bias at mainstream media there's an article in Wikipedia about Media coverage of the Arab–Israeli conflict but it's contradictory because it consists claims of bias from both pro-Palestinian and Pro-Israel watchdog groups.