In the disk-mediated accretion scenario for the formation of the most massive stars, gravitational instabilities in the disk can force it to fragment. We investigate the effects of inclination and spatial resolution on observable kinematics and stability of disks in high-mass star formation. We study a high-resolution 3D radiation-hydrodynamic simulation that leads to the fragmentation of a massive disk. Using RADMC-3D we produce 1.3 mm continuum and CH3CN line cubes at different inclinations. The model is set to different distances and synthetic observations are created for ALMA at ~80 mas resolution and NOEMA at ~0.3. The synthetic ALMA observations resolve all fragments and their kinematics well. The synthetic NOEMA observations at 800 pc (~300 au resolution) are able to resolve the fragments, while at 2000 pc (~800 au resolution) only a single slightly elongated structure is observed. The position-velocity (PV) plots show the differential rotation of material best in the edge-on views. As the observations become less resolved, the inner high-velocity components of the disk become blended with the envelope and the PV plots resemble rigid-body-like rotation. Protostellar mass estimates from PV plots of poorly resolved observations are therefore overestimated. We fit the emission of CH3CN lines and produce maps of gas temperature with values in the range of 100-300 K. Studying the Toomre stability of the disks in the resolved observations, we find Q values below the critical value for stability against gravitational collapse at the positions of the fragments and the arms connecting the fragments. For the poorly resolved observations we find low Q values in the outskirts of the disk. Therefore we are able to predict that the disk is unstable and fragmenting even in poorly resolved observations. This conclusion is true regardless of knowledge about the inclination of the disk.
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