The significant influence of adsorbate interactions in surface dynamics is quantified using mean-field approximation (MFA) and quasichemical approximation (QCA) approaches and two typical situations (i) T > T-c (critical temperature for surface phase transformation) and (ii) T < T-c are analyzed. The formulation involves transition state theory (TST) and the key parameters involved are : (1) the sign and magnitude of the pairwise adsorbate interaction energy (w > 0, w < 0 meaning repulsive and attractive interactions, respectively) (2) W-A#, the interaction energy between a molecule in the ground state and the activated complex. W-A#(A) is in turn related to w by a coupling parameter sigma. sigma=0, sigma=1 are shown to result in extreme divergence of the rate behavior for both repulsive and attractive interactions. First T > T-c is considered. For sigma=0, attractive interactions retard and repulsive interactions enhance the surface rates. The rates display nonmonotonic behavior for attractive interactions and steady increase with surface coverage for repulsive interactions. However, when sigma=1, the rates monotonically increase for both types of forces. In addition the attractive forces show an instability of the slope due to a cooperative catalytic effect. Both attractive and repulsive forces display maxima when plotted against temperature, the maxima being sharper for the former case. The case T < T-c is more interesting, as a discontinuous phase separation can occur for attractive interactions. The density and internal energy differences between the coexisting phases are computed proceeding from closed-form expressions of the canonical ensemble partition functions and employing standard methods of statistical mechanics. Since repulsive forces can only show continuous order-disorder transitions, they are not considered for T < T-c. The surface rate expressions (both corrected and uncorrected for ground-state internal energy differences between the phases) display a symmetric rate curve (symmetric about theta=0.5) vs surface coverage with a maximum at theta=0.5. A certain type of hole-particle symmetry is present in the rate expression as the rate expression is invariant with respect to the exchange of an occupied and vacant site. This conclusion is valid for both sigma=0, sigma=1. The appearance of symmetry in the rate curve is suggestive of the phase separation. The qualitative differences between the rate predictions of MFA and QCA are significant enough to warrant refinement in the analysis of surface dynamics.