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In one of the episodes from Carl Sagan's show Cosmos he explains that Beta Andromedae is the second brightest star in the constellation Andromeda, and is 75 light years away. The link to the video is here.

I've looked up this star on Wikipedia and it says it's the brightest star in the constellation, not the second brightest, and instead of 75 light years away it says it's about 197 light years away.

I know that this show Cosmos is quite old. It aired in 1980. I understand our measurements are more accurate nowadays, but I was just wondering if anyone knew why the discrepancy with the brightest and second brightest star claims, and also that the Wikipedia article says it's 197 light years away, a difference of about 260% from the 75 light years mentioned by Sagan. That's quite a significant difference.

His information of the distance from us to the center of our galaxy is quite close: he says 30 thousand light years; Wikipedia says 27 thousand light years. As to our distance to Andromeda, he says: 2 million light years; Wikipedia says 2.5 million light years.

Have I completely got the wrong star that I'm looking up?

I think I found the source of the 75 light year distance for Beta Andromeda as being from the 1978 edition of Burnham's Celestial Handbook

From this excerpt out of Google Books

Name - Mirach. Mag 2.03 ... The distance is about 75 light years according to parallaxes obtained at Mt. Wilson, Allegheny, and McCormick; the resulting luminosity is about 75 times that of the Sun, and the absolute magnitude about +0.2.

Just reading the excerpt alone, I'm unclear if this is a misinterpretation of the results from the observatories or that at the time the understanding the characteristics of star type would result in the discrepancy.

Distances of stars measured by parallax in general (and red giants in particular) can be notoriously inexact, and the distance values can vary markedly between different measurements. For example, Betelgeuse has been measured as being 520±73 ly by the Hipparcos mission, and 643±146 ly by the Very Large Array.

I often find distances to stars listed on wikipedia are different from what I remember them to be a decade ago.

Mirach is a red giant star. It is entirely possible that the measurements may have changed considerably in that time.

Looking at the SIMBAD data page for Beta Andromeda shows the source of both the parallax (distance) and the magnitudes. In this case, as it will be for many bright stars, the source of the parallax is the reprocessed data from the Hipparcos satellite, described in this paper. Prior to the launch of the Hipparcos satellite by ESA in 1989, parallaxes were very difficult to obtain and only low precision values were available for the closest stars.

The parallax given in SIMBAD for Beta Andromeda is $16.52pm0.56$ milliarcseconds which translates to a distance of $60.5pm2.1$ parsecs or $60.5times3.26=197$ light years. This small parallax would have been extremely challenging or impossible to measure accurately with the pre-CCD technology before 1980. Errors of several hundred percent were not uncommon. The prior parallax measurement which probably was an improvement on what was available in 1980 at the time of Cosmos is from van Altena et al. 1995. This lists a parallax of $47.7pm7.9$ millarcsec, a nearly 5x larger error and which gives a distance of 68 light years.

Similarly we can see that the $V$-band magnitude comes from this collection and the difference between Beta Andromeda ($V=2.05$) and Alpha Andromeda ($V=2.06$), the in-theory brightest star in the constellation is only 0.01 magnitude. Measuring a star that bright to that precision was, and in fact still is, quite difficult as most detectors will saturate. So it's not particularly surprising given how close Alpha and Beta Andromeda are in brightness, that the early measurements got them reversed when Beta is in fact (very slightly) brighter.

This high brightness probably means that we will not see a more accurate from the Gaia satellite, the successor to Hipparcos. The Gaia DR2 data release lists a brightness limit of $Gsim3$ which may be improved slightly in later data releases with more sophisticated data processing and treatment of saturated stars.