The gemara discusses the proper order for the parshiyos of tefillin. Rashi interprets that the order is: קדש, והיה כי יביאך, שמע, והיה אם שמוע. But Rabbeinu Tam disagrees with rashi's reading of the gemara and says that it is קדש, והיה כי יביאך, והיה אם שמוע, שמע. It is interesting to note that even those who wear tefillin of Rabbeinu Tam aren't really fulfilling the mitzvah according to Rabbeinu Tam because Rabbeinu Tam brought in Tosafos 33a holds that the parshiyos have to be lying down in the tefillin, not standing upright, just like he holds by mezuza. It is clear from the gemara by mezuza that if it's placed upright according to Rabbeinu Tam, it is passul. Since Rabbeinu Tam assumes the same halacha should apply to tefillin, the placement of the parshiyos upright would invalidate the tefillin.
Rav Moshe (Igros Moshe O.C. 4:9) was asked by the Lubavitcher Rebbe why he doesn't wear Rabbeinu Tam tefillin. Rav Moshe responds very sharply that the minhag of sofrim in writing tefillin nowadays seems to be against the halacha in the way that they do the פתוחות and סתומות. Rav Moshe explains that when it comes to tefillin of Rashi who everyone agrees is the ikar, we have no choice but to wear what is available. But, regarding R"T, since it is only a chumra, he is only willing to wear it if it is done according to his standards.
To understand R. Moshe's reservation, it is necessary to understand the rules of פתוחות וסתומות. All agree that if the first paragraph would end in the middle of a line with space of 9 letters left and the next parsha begins at the start of the next line, it is a pesucha. All agree that if there is space of 9 letters left in the middle of a line separating between two parshiyos, that is a setuma. If the first parshah doesn't leave space of 9 letters and the second parsha begins at the start of a line but there is a blank line in between, the Rosh considers it a setuma and the Rambam considers it a pesucha. If the first parsha goes to the end of the line and the second begins with an indentation of 9 letters, that is setuma according to the rambam but pesucha according to the Rosh. The halacha is that the parsha of והיה אם שמוע needs to be a setuma. The Shulchan Aruch (32:36) explains that since we can't write them in the same paragraph, it is impossible to do a setuma according to everyone. Therefore, we have no choice but do pick the Rambam or the Rosh. We follow the Rambam and do a setuma by not leaving 9 letters of blank space after שמע and indenting with a space of 9 letters the parsha of והיה אם שמוע. The problem is that the sofrim leave 9 letters of blank space after the parsha of shema AND before והיה אם שמוע. Rav Moshe holds that leaving blank space at the end of the parsha preceeding והיה אם שמוע indicates an interest in making a pesucha, and then indenting at the beginning of והיה אם שמוע indicates a setuma which creates a תרתי דסתרי. He considers this to be a potential p'sul, and wasn't willing to wear Rabbeinu Tam tefillin unless they are makpid not to leave space of 9 letters at the end of the parsha that proceeds והיה אם שמוע (which according to Rabbeinu Tam is והיה כי יביאך).
R. Moshe writes that the source for this custom of leaving 9 letters both at the end of the previous parsha and before והיה אם שמוע comes from the kunteros acharon in shulchan aruch ha'rav where it says in parenthesis that the ba'al hatanya retracted from his original agreement to shulchan aruch and commanded the sofrim to leave space both at the end of the parsha proceeding והיה אם שמוע and at the beginning of והיה אם שמוע. Rav Moshe notes that there is no explanation for such an opinion and strongly rejects it. However, in the very first teshuva printed in the back of the shulchan aruch ha'rav he justifies this position by saying that according to the Rambam that indenting 9 letters in the parsha of והיה אם שמוע creates a setuma, it makes no difference whether in the previous parsha there was space of 9 letters left or not. Apparently, Rav Moshe didn't see this teshuva of the shulchan aruch ha'rav.