Mizmor Shir Chanukas Habayis

According to minhag Ashkenaz Mizmor Shir was never said.
The saying of Mizmor shir was accepted according to the Sephardi minhag, and the Ariz"l explained it according to the Kabboloh. But according to Minhag Ashkenaz the place to have the mizmor is after Hodu, and there we say Mizmor Lesodah, therefore there is no place for Mizmor Shir over there.
And in addition to this point, the Tur (in אורח חיים, siman נא) brings that there are two minhogim regarding "Hodu". Some say "Hodu" before Boruch She'omar (the Sephardi minhag), and some say it after(Minhag Ashkenaz), and the Tur concludes, that the better way is to say it after Boruch She'omar, because in this way the mizmorim in which we praise Hashem have a Brocho before them (unlike if you say Hodu beforehand - Hodu doesn't have a brocho before it). For the same reason there would be a problem to say Mizmor shir before Boruch She'omar.

Michael