In reporting distances of galaxies, what are the typical error bars and associated confidence levels?
The error bars are typically very large.
There are several ways of determining the distance of galaxy:
Cepheid variable stars have a known relationship between luminosity and period. If we can observe these variables as individual stars in a galaxy, we can determine distance.
But individual stars can only be observed in the nearest galaxies. This method can't determine the distance of galaxies in which we can't resolve individual stars.
There is about +-7% uncertainty, plus possible systematic errors (wikipedia gives a distance modulus uncertainty of 0.16 for an individual galaxy, and states that the uncertainty in distance can be calculated as 0.461 x distance modulus uncertainty = 0.07)
Type 1a supernovae
These have a known and fixed luminosity (of about magnitude -19.3) If we can observe a supernova of the right type in a galaxy, we can tell how far it is.
But to use this method we have to wait for a supernova, and even in the larger galaxies they are rare. Also the "known luminosity" has to be calibrated against Cepheid variables, so there might be systematic errors.
A well-observed supernova can fix the distance with uncertainty of about 5%, however there may be systematic errors.
Association with other galaxies
If two galaxies are interacting then we know that they must be about the same distance, if we can measure one, (by supernova) we get an estimate of the distace of the other.
Distant galaxies are receeding from us and E. Hubble observed that there is a correlation between the redshift caused by the galaxy moveing away from us, and the distance. So for more distant objects we can use the red-shift as a proxy for distance.
However the peculiar motion of the galaxy also causes red (or blue) shift and this is not know. The calcualation of distance depends on the observed constant of proportionality, and while this is about 70 the exact value is not known (and probably not constant) This method can't be used for local galaxies.
Systematic errors are due to uncertainties in the models being used. For example the nearby cepheid variables tend to be from stars with lots of carbon, nitrogen and other elements (besides H and He). These have a different luminosity from stars formed with little except H and He. Cepheid variables were used to measure the size of the milky way, assuming that the stars being measured were like the nearby stars. They were not. Correcting this systematic error resulted in distances that were double what they had been previously. The calculated size of the milky way doubled!
So if someone says This galaxy is 50 million light years away, you can be reasonably confident that it is somewhere between 30 and 80 million light years away. And perhaps more confident if there has been a recent supernova there.