Spin-orbit effects in single-electron states in laterally coupled quantum dots in the presence of a perpendicular magnetic field are studied by exact numerical diagonalization. Dresselhaus (linear and cubic) and Bychkov-Rashba spin-orbit couplings are included in a realistic model of confined dots based on GaAs. Group theoretical classification of quantum states with and without spin-orbit coupling is provided. Spin-orbit effects on the g factor are rather weak. It is shown that the frequency of coherent oscillations (tunneling amplitude) in coupled dots is largely unaffected by spin-orbit effects due to symmetry requirements. The leading contributions to the frequency involves the cubic term of the Dresselhaus coupling. Spin-orbit coupling in the presence of a magnetic field leads to a spin-dependent tunneling amplitude, and thus to the possibility of spin to charge conversion, namely, spatial separation of spin by coherent oscillations in a uniform magnetic field. It is also shown that spin hot spots exist in coupled GaAs dots already at moderate magnetic fields, and that spin hot spots at zero magnetic field are due to the cubic Dresselhaus term only.