This work presents issues related to selected errors accompanying spatial measurements of surface roughness using contact profilometry. The influence of internal heat sources, such as engines or control electronics, on the thermal expansion of the drive responsible for the measurement probe’s movement in the X-axis direction was investigated. In terms of starting measurements on a thermally unstable device, the synchronization error of individual profile paths was 16.1 µm. Based on thermographic studies, the time required for full thermal stabilization of this drive was determined to be 6–12 h from when the device was turned on. It was demonstrated that thermal stabilization of the profilometer significantly reduced positioning errors of the measurement probe on the X-axis. Thermal stabilization time should be determined individually for a specific device variant. This research also determined how changes in the center of gravity caused by the measurement probe’s movement affected the overall rigidity of the profilometer structure and the leveling of the tested surface. Laser interferometry was used for this purpose. The determined vulnerability of the profilometer structure was 0.8 µm for a measurement section of 25 mm. Understanding the described relationships will reduce errors associated with conducting measurements and preparing equipment for tests. Additionally, it will enable the correct evaluation of surface geometry.