The Astronomy isn't terribly bad (at least not as bad as most of these "religion is all star based" claims). Sirius does lines up with those three stars every day of the year, which I've heard called "The Three Kings" once - and not by someone in astronomy. Orion and Sirius are early Fall constellations, which means on December 25 they are setting as the sun is rising. However it is true that if you look at the stars at their rising and follow the line from those three stars through Sirius, you get a specific point on the horizon and 12 hours after these stars pointed to that point on the horizon, the sun will rise at that point.
He does misrepresent a point later, about the sun being "in the vicinity of the southern cross" on December 25 when it stays put for "three days". Cute. I suppose if you consider "vicinity" half the sky away, sure! The southern cross is a, ahem, southern constellation and although the sun is close, it's closest to it near the end of January (in the year zero - in the year 2007 it's February). I certainly wouldn't consider it in the vicinity as it's practically 40 degrees away.
He would have done better to point out that it was "between the southern and northern cross (the norther cross is another name for the constellation Cygnus the Swan)". But even then it's more directly in between those in January and it wouldn't have had the same effect of putting the sun ON the cross (which it never is). You would think someone who studied astrology would know which constellations the sun was in. In December the Sun rises in the constellation of Sagittarius (the teapot or archer), or if you go back to the time of Christ it will be in Capricorn. The Sun rises in Virgo around August (when most Virgo's are born).
I also loved how he reduced the "astrological sign" to the cross with the halo then went through painstaking care to only show crosses with the halo around it. See it's the same! Oh and the part about the crown of thorns was great - he would have done better to point out that the sun's "crown of thorns" or halo is most visible during a solar eclipse, when "darkness is prevailing over the light." That would have been a cool touch.
It would be interesting to know how much of his history is correct about those other religions. I liked your point about how other pagan religions would by nature prefigure Christianity. I personally would be more worried if there was no evidence for Christianity in nature or in other religions, for if something is totally new, then it is almost guaranteed to be false.