The circumgalactic medium (CGM) of the Milky Way is mostly obscured by nearby gas in position–velocity space because we reside inside the Galaxy. Substantial biases exist in most studies of the Milky Way's CGM that focus on easier-to-detect high-velocity gas. With mock observations on a Milky Way analog from the Figuring Out Gas & Galaxies in Enzo (FOGGIE) simulation, we investigate four observational biases related to the Milky Way's CGM. First, QSO absorption-line studies probe a limited amount of the CGM mass: only 35% of the mass is at high Galactic latitudes , of which only half is moving at . Second, the inflow rate () of the cold gas observable in H i 21 cm is reduced by a factor of ~10 as we switch from the local standard of rest to the galaxy's rest frame; meanwhile, the of the cool and warm gas does not change significantly. Third, O vi and N v are promising ions to probe the Milky Way's outer CGM ( kpc), but C iv may be less sensitive. Lastly, the scatter in ion column density is a factor of 2 higher if the CGM is observed from the inside out than from external views because of the gas radial density profile. Our work highlights that observations of the Milky Way's CGM, especially those using H i 21 cm and QSO absorption lines, are highly biased. We demonstrate that these biases can be quantified and calibrated through synthetic observations with simulated Milky Way analogs.