Accuracy of the different levels of electronic structure theory is frequently studied for stationary-point properties; however, little is known about the effects of the electronic structure methods and basis sets on the dynamics of chemical reactions. Here we report such an investigation for the F- + CH3I S(N)2 and proton-transfer reactions by developing 20 different analytical potential energy surfaces (PESs) obtained at the HF/DZ, HF/TZ, HF-D3(BJ)/DZ, HF-D3(BJ)/TZ, MP2/DZ, MP2/TZ, MP2-F12/DZ, MP2-F12/TZ, CCSD/DZ, CCSD-F12b/DZ, CCSD(T)/DZ, CCSD(T)-F12b/DZ, OQVCCD(T)/DZ, B97-1/TZ, PBEO/TZ, PBEO-D3(BJ)/TZ, M06-2X/TZ, M06-2X-D3(0)/TZ, B2PLYP/TZ, and B2PLYP-D3(BJ)/TZ levels of theory, where DZ and TZ denote the aug-cc-pVDZ and aug-cc-pVTZ basis sets with a relativistic effective core potential and the corresponding bases for iodine. Millions of quasiclassical trajectories on these PESs reveal that (a) in the case of standard methods, increasing the basis from DZ to TZ decreases the S(N)2 cross sections by 20-30%; (b) the explicitly correlated F12 reactivity is converged with a DZ basis; (c) the quasi-variational OQVCCD(T) and the CCSD(T) methods provide virtually the same cross sections; (d) the above DFT functionals give significantly larger S(N)2 cross sections than the ab initio methods; (e) retention S(N)2 cross sections show striking method and basis dependence and double inversion is substantially enhanced with a TZ basis or F12 methods; (f) the TZ basis doubles the DZ proton-transfer reactivity; (g) at a high collision energy ab initio methods show dominance of backward scattering, in agreement with experiment, whereas most DFT functionals provide slight forward preference; and (h) at high energy the ab initio correlation (DFT) methods slightly underestimate (overestimate) the CH3F internal energy excitations, whereas the broad experimental distribution is qualitatively reproduced.