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In brief the filibuster gives any Senator 1/40th of a say over an appointment instead of 1/50th.
That gives a Senator more leverage for swapping his vote for whatever he wants to trade it for.

From the AP article:

GOP Senator Warns Bush on Anti-Abortion Justices
By LARA JAKES JORDAN, AP

PHILADELPHIA (Nov. 4) - The Republican expected to chair the Senate Judiciary Committee next year bluntly warned newly re-elected President Bush on Wednesday against putting forth Supreme Court nominees who would seek to overturn abortion rights or are otherwise too conservative to win confirmation.

Sen. Arlen Specter, fresh from winning a fifth term in Pennsylvania, also said the current Supreme Court now lacks legal "giants" on the bench.

"When you talk about judges who would change the right of a woman to choose, overturn Roe v. Wade, I think that is unlikely," Specter said, referring to the landmark 1973 Supreme Court decision legalizing abortion.

"The president is well aware of what happened, when a number of his nominees were sent up, with the filibuster," Specter added, referring to Senate Democrats' success over the past four years in blocking the confirmation of many of Bush's conservative judicial picks. "... And I would expect the president to be mindful of the considerations which I am mentioning."

Specter MUST not chair the Senate Judiciary Committee.

In brief the filibuster gives any Senator 1/40th of a say over an appointment instead of 1/50th.

I think it just gives the minority party undiserved leverage against the majority.