(This is an improved version of a short post published in '07.)
See Magen Avraham 8:6, who brings from the Shelah that you should have an atarah (something that indicates where the top is, not a bullfighter's traje de luces) on a tallis so the part that goes on the head will not be mistakenly switched to the other side, based on the rule that maalin bakodesh v’lo moridin; just as we find that the krashim of the Mishkan were marked so the kerashim of the north side, which has greater kedusha, should not be switched to south. So, too, the part that goes on your head has a greater chashivus than the part that hangs on the bottom.
The Magen Avraham, however, holds like the Ari zal, that there is no such kpeida, and you can turn the tallis any way you want. See also the Magen Avraham in Siman 42, who says that it is asur to reverse the retzu’ah shel yad so the part that had the kesher is now on the fingers, because ein moridin.
(Obviously, retzu'os are not kedusha atzma, despite the Gemara in Shabbas 62a, because, as Tosfos says there and in Menachos 35b, with proof from Megilla 26b. Also the Rambam calls the letters in the retzu'os just keshorim in the form of letters, and not real kisvei kodesh, as the Griz says on the Rambam. And even Rashi that calls them 'osiyos' just means that they have the form of osiyos, not real kisvei kodesh. As the Rogotchover says in his Tzofnas Pa'anei'ach, the Gemora in Eiruvin 97b says that one who makes letter keshorim on shabbos is only chayov for kosheir and not for koseiv. [A rayoh one can ding zach on, by the way.] So the point is that retzu'os are not kisvei kodesh/kedusha atzma. But also obviously, there's a difference between the retzu'os, about which it says (Shabbos 28b) "lo huchsheru limleches shomayim eloh ohr beheima tehora, and the beged of a tallis. Also obviously, there's a difference between a tzuras ohs on a retzu'ah and the beged of a tallis. So its not surprising that the MA is makpid on ein moridin in the case of retzu'os.)
The Shaarei Tshuvah there brings that the grandfather of the Eliya Rabba brought a rayah from our parshah against the Shelah, and even against the Magen Avraham’s chumroh by the Retzu’ah. Chazal say that when Yaakov took some stones to place under his head, the stones fought among themselves for the merit of being the pillow of the tzadik. To settle their well-meaning dispute, Hashem made turned the many stones into one stone. We see, he says, that the stones only fought when it was a question of one or the other being directly under Yaakov's head. But once they became one stone, there was no longer an issue of what part of the stone Yaakov lied on, because it doesn’t matter. Within an object itself, there is no din of ein moridin.
Here you have the ER bringing his grandfather's opinion that you can bring a raya, and the Shaarei Teshuva that absolutely rejects the idea of bringing a raya from agada.
However, the argument can be made that this agada about Yaakov's stone pillow is a valid rayah, because nobody takes the story about arguments among stones literally, so it must be meant homiletically. Homiletical devices must be crafted so as to square with the halachah. On the other hand, it could be that the agadeta was stated by a tanna whose opinion has no standing in halachah l’maiseh, and was kept only for its mussar or message value– that inanimate nature itself strives to serve a tzadik. Accepting a psak is different than accepting a drush. Psak has to be consistent with other psakim and emes l’amito. Drush just needs a message that is true for some people in some circumstances. It’s like the difference betweeen halacha and halacha l’maiseh.