One of the oblivion loading texts says he`s a direct descendant of Tiber Septim. However AFAIK the Septim line is fractured, with Tiber Septim`s direct descendants ending fairly early in the empire. Did I miss some ambiguity or is the text an error?

Well, he certainly seems to have been related to Tiber.
But a "direct descendant"? No. Tiber's line ended very early; the next emperor after him was his grandson Pelagius, and Pelagius died childless.
According to the Brief History the Empire: "Pelagius had no living children, so the Crown Imperial passed to his first cousin, the daughter of Tiber's brother Agnorith, Kintyra."

You know I don't understand why there covenant with Akatosh and Alessia stood past her death, given it says "as long as one of your decendents wares this amulet..." but Tiber and his family isn't a decedent of Alessia are they?

No, the Septims weren't related to either Alessia or Reman.
I don't understand it either; that covenant has never made sense to me.

ahh, see that's why I don't understand the whole Amulet of Kings in relation the Emperors, and thus, the main quest of Oblivion heh.

Well my thought on this issue is that person must be a dragon born, which after the skyrim trailer makes me think the title refers to exceptional/important individuals (yes I know great source) as opposed purely to a bloodline. Admitably this is pure conjecture on my part.

[font="Georgia"]Soo Alessia would have been a Dragonborn? just by odd chance? as well as Remen?/font]

Not by odd chance.
And Reman has a link to Alessia through his mystical birth.

http://imperial-library.info/ForumArchives/Amulet_of_Kings.htm

My thought was basically the devs are expanding the definiton to of dragon born and the conotations that come with it. The expansion, if it plays out in the way that it looks like it is going to, represents the idea that the person is a leader and/or champion of man. Such a positon would be similar to that of Akatosh in relation to men, thus they are Dragon Born.