Estimated distances to nearby galaxies such as NGC 300 seem to be fairly accurate. This is because astronomers measure using "standard candles" called Cepheid Variable Stars. This is a class of giant stars which are periodic variables, with very regular fluctuations. The periodicity depends on the brightness (which depends on mass). Brighter equals slower. Thus if we know how BRIGHT the star is at, say, a standard distance (absolute magnitude), we can determine a distant Cepheid's brightness (apparent magnitude) and so figure the galaxy's distance. We know how bright the Cepheid SHOULD be by its period of variability.
The fly in the ointment, so to speak, is the presence of intergalactic dust which will absorb some light. Measurements at various wavelengths on the electromagnetic spectrum may help to determine the amount of absorption.
Typical light curve for a Cepheid variable star
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