As you no doubt know, the filioque is the phrase "and from the Son", referring to the procession of the Holy Spirit. This belief is also known as the "double procession" of the spirit.
The Orthodox Church has a number of problems with the filioque. Some are canonical, relating to the manner in which the filioque came to be incorporated in the creed. More importantly, however, we view the double procession as a misunderstanding of the trinitarian nature of God. As Jesus taught, God is the father and the source of the Godhead; Jesus, not being a source of the Godhead (although He is God), cannot be the source of the Spirit (which is also God). Jesus *sends* the Spirit, but it does not *proceed* from Jesus.
Orthodox theology views the triune God as rather like a triangle, with the Father at the point. The filioque turns the triangle 90 degrees, and places Jesus and the Father at the top, and the Holy Spirit at the bottom.