Re: "Does this mean that a star's declination for instance that of Vega at 8000 BC can be off by a whopping 2.6 degrees?"
--No, I don't think that much off. What that table is doing, is comparing the polynomial expansion methods, taken out to differing extents (T**10 instead of T**6), so the long times have much bigger errors. I think the early versions of Starry Night were off by that much, but the newer versions are better by that much. But as Starry Night said today, they found errors in the newer version too.
The problems actually arise, generally, because Starry Night uses the polynomial expansion method, instead of the Fourier expansion method. The former can be extremely accurate for years/millennia around the present but then fall off rapidly over long times, if they are not careful. Starry Night says they now use the Method of Williams (1994), but I am reading that paper and he also says Williams (1994) says, “The polynomial expressions in Table 5 can be used for times extending out to a few millennia, but are not suitable for longer times. The polynomials are equivalent to expansions of expressions appropriate for longer times: an average precession rate and obliquity plus long-preiodic, or at least quasiperiodic, terms with periods exceeding 10,000 yr (Berger 1976; Laskar et al. 1993). ...”
Berger 1976, as I told Starry Night, is the method I use. We'll have to see what Starry Night comes out with in their fix. I think, for Vega circa 12000 BC, they will find the correct declination is closer to the value I quoted (about 0.3 degrees higher), but we'll see...