Rheometers have made giant leaps in terms of usability, sensitivity, and versatility. This leads to the illusion that a rheometer can be used as a fool-proof device for measuring rheological properties. The article will focus on typical problems that are encountered in rheological practice when measuring polymer melts. Emphasis is put on problems related to measurement artefacts stemming from the rheometer as well as from the material itself. Furthermore, possibilities to eliminate rheometer related artefacts mostly related to the following phenomena - geometry inertia, thermal expansion, torque resolution, and environmental control - will be discussed. The sample related artefacts vary significantly from sample to sample and include: thermal degradation, nonlinear shear deformation, centrifugal forces, slip and shear banding, as well as miscibility, orientation, and distribution of different phases, of which only the ones occurring in homogeneous polymer melts are discussed here.