Is the prayer valid if there are spots of impurity (feces) on the mosque carpets, and one moves approximately a meter away from them before praying?

The presence of stains on carpets does not affect the validity of the prayer of one who prays on them, as long as the spot on which the person is praying is pure. This is because the purity of the place, which is a condition for prayer, refers to the area directly touched by the worshipper, not what is around it.