The astrometric solution for Gaia EDR3 and its properties are discussed in detail in Lindegren et al. (2021). In addition, the complex issue of the parallax zero point is addressed in Lindegren et al. (2020), and the reference frame in Klioner et al. (2020). Various validation tests are presented in Fabricius et al. (2021) including studies of the negative parallax tail.
A tricky issue for Gaia EDR3 astrometry is that some sources have a 5-parameter solution and others a 6-parameter solution, depending on whether reliable photometry was available in Gaia DR2. When this is not the case, a sixth parameter, the pseudocolour was included. This typically happens for sources in crowded regions and in some narrow strips where the scan coverage was poor in Gaia DR2. It is therefore not a priori clear whether poorer quality for a set of 6-parameter solutions is caused by the additional parameter or by the conditions that prevented the sources from obtaining reliable colours.
Another important issue is the spurious solutions with unrealistic values for proper motion and parallax. A clear example are the 3 million sources with negative parallax and an uncertainty more than five times smaller. This issue is addressed in Fabricius et al. (2021).
In Gaia EDR3 all sources were assumed to be isolated point sources. This assumption is of course not always valid. A number of indicators help identifying these cases. This question is also addressed in Fabricius et al. (2021).
One such indicator is the goodness of fit of the astrometric solution. Since Gaia DR2, the definition of astrometric_gof_al has changed, as it now uses the ruwe, and is thus much less sensitive to calibration errors for bright stars, and more indicative of a potential non-single star nature. Although the astrometric_gof_al behaves as expected for contaminated sources, almost flat with magnitude (see Figure 8.5) the goodness of fit for sources without excess noise is not realistic.