During the production of components, manufacturers of structures are obliged to meet certain requirements and ensure appropriate quality characteristics. It is especially important during the manufacturing of thin-walled structures, which are subject to many errors during machining due to the reduced rigidity of the products, including the deformation of thin walls, which may be the result of the vibration of the system. The appearance of vibrations reduces the quality of the machined surface affecting the increase in the values of surface topography parameters—waviness and roughness. Thin-wall structures—titanium or nickel alloy, among others—play a key role in the aerospace industry, which constantly strives to reduce the weight of the entire structure while meeting requirements. The present work focuses on the evaluation of the parameters of surface topography, dimensional and shape accuracy during the milling of nickel alloy Inconel 625 samples containing a thin wall in a vertical orientation. The experiment was conducted under controlled cutting conditions using a constant material removal rate. As part of the surface topography section, the distribution of waviness, Wa and Wz, and roughness, Ra and Rz, was determined in selected measurement areas in the direction parallel to the direction of the feed motion. Dimensional deviations, measured with a 3D optical scanner, were determined in selected cross sections in the direction perpendicular and parallel to the bottom of the sample presenting the deflection of the thin-walled structure. The results provide information that the used parameter sets affect the measured quantities to varying degrees.