Nonequilibrium molecular dynamics (NEMD) simulations are used to investigate the behavior of a fluid of dipolar Lennard-Jones (LJ) particles under planar Couette flow. Such systems can be viewed as simple models for magnetic ferrofluids. Various issues that arise in such simulations are discussed. These include the importance of the long-range dipolar forces, the influence of different thermostats, and the induction of orientational order. The shear viscosity is found to be somewhat sensitive to the treatment of the dipolar interactions with spherical truncation giving lower values than Ewald sums. The system considered is characterized by a moderate dipole moment, and strong orientational order does not develop at low shear rates. However, the direction of the weak polarization correlates with the shear-induced distortion of the fluid structure. At very high shear rates the fluid behavior depends on the thermostat applied. While the results are not strongly sensitive to details of the rotational thermostat, this is not the case for translational motion. A translationally biased thermostat leads to a string phase, although string formation requires significantly higher shear rates for the dipolar fluid than for the corresponding LJ system. For the dipolar fluid, the string phase is accompanied by strong orientational ordering perpendicular to the flow for Ewald sums and with the flow for the spherically truncated case. In the Ewald systems the order was ferroelectric for conducting boundary conditions, and an antiferroelectric domain structure formed in the vacuum case. For the truncated potential individually polarized chains are randomly oriented with or against the flow. The string phase and the orientational ordering disappears when the translationally unbiased thermostat of Evans and co-workers is employed. Some NEMD simulations with oscillating shear were also performed. These yielded layer structures and again strong orientational order in the dipolar case.