We investigate the dynamics of splay-phase states, special out-of-phase states, in an array of globally coupled phase oscillators. Using asymptotic methods and a dimension reducing coordinate transformation we derive explicit representation for saddle shaped surfaces on which the dynamics is confined. The restricted motion is due to a high degree of neutral stability possessed by the splay-phase and related incoherent states. An additional consequence of the neutral stability is an extreme sensitivity to intrinsic noise which leads to diffusive drift. The elimination of this drift motivates an examination of the effect of parameter perturbations and their use for control. We have found that the system is uncontrollable using symmetry-preserving perturbations, but that symmetry-breaking perturbations effectively allow for the prevention of noise-induced drift. Finally, we have made observations on how general disorder affects the dynamics of the system; in particular, for small disorder certain sums of the phases become unbounded while others remain fixed.