Excited states have been studied in 35Ar following the 16O(24Mg,1alpha1n)35Ar fusion-evaporation reaction at 60 MeV using the Ge-detector array GASP. A comparison with the mirror nucleus 35Cl shows two remarkable features: (i) A surprisingly large energy difference for the 13/2(-) states, in which the hitherto overlooked electromagnetic spin-orbit term is shown to play a major role, and (ii) a very different decay pattern for the 7/2(-) states, which provides direct evidence of isospin mixing.