The Raving Atheist may be playing devil's advocate — one never can quite tell with him — but he appears to be saying that Catholics hold many doctrines that make them non-Christian, including Mary worship.
I think that all his criticisms deserve to be taken seriously and not just written off as the complaints of an antireligionist. They're about the same issues that kept me from entering the Church for years. Someone who's looking for straightforward Bible-based answers to them would do well to pick up a copy of the Catechism, which I'm reading now. It is beautifully written and very profound.
My understanding of Mary's place in Christian life developed largely though reading St. Maximilian Kolbe's writings about her. An article on CatholicCulture.org encapsulates them well.
I'm uncomfortable doing apologetics for prayer that invokes Mary; the line between worshiping her and asking her for prayer seems meaningless when one tries to explain it to a non-Catholic. But I do love her and pray that I will grow in understanding of her.
I believe that God hears all prayers to Him, regardless of whether they are in Jesus' name. At the same time, I believe that if one believes Jesus is Lord, one is compelled to pray in His name, because it signifies a desire to unite one's will to His. Addressing prayer to Mary, in turn, makes me want to unite my will to hers, which is always united to Jesus'.
Certainly I could just pray to Jesus, but I gain a different — and, often, more needed — spiritual benefit from envisioning Mary and the particular qualities which she embodies, including her sacrificial love, her humility, and her wisdom. Again, Jesus has all those qualities as well, yet I feel better able to emulate Jesus through emulating Mary's perfect reflection of His grace.