I sweat a lot and it occurs that I wipe the sweat from my face with my hands during prayer. Is this a problem as far as the need of having clean hands during prayer?

There is no Halachic problem with this, as the Shulchan Aruch (Orach Chaim 4, 21) writes: One should be careful while praying or eating not to touch his leg, thigh or covered places since there are particles of sweat there. One should also not scratch his head, but one does not have to be particular with revealed places in one’s head and face and in the revealed part of his arms. The Mishnah Berurah (ibid 52) refers to Yoreh Deah 116 that one should avoid sweat, as every sweat is poison except for facial sweat, as is indicated: “With the sweat of your face you shall eat bread”.