1) The Rambam writes in Hil Beis HaBechira (1:12):
והכל חייבין לבנות ולסעד בעצמן ובממונם אנשים ונשים כמקדש המדבר.
"Everyone has to participate in the mitzvah of building a mikdash, both men and women, just like all participated in building the Mishkan in the desert."
Why does the Rambam add that last phrase? Why can't he just say that men and women must participate -- why add the comparison to the Mishkan?
2) According to Chazal the "bri'ach ha'tichon," the central beam that went through the middle of all the boards of the Mishkan, miraculously curved itself around the entire structure. Where did this special beam come from? Targum Yonasan (26:28) writes that it came from the tree planted by Avraham, "Va'yita eisehel b'Be'eir Sheva," to provide shade and a place to rest for his guests. When Klal Yisrael left Egypt the angels came and cut down that tree, threw it into Yam Suf, and from there it was retrieved by Bnei Yisrael.
Why did the angels bring davka that tree? Was there no closer place to get wood from? R' Yaakov Kaminetzki has a wonderful insight regarding the "atzei shitim," which Chazal tell us were planted by Yaakov Avinu (see my son's post here). The gemara (Yoma 72) writes that the word "omdim" used to describe these boards means they are eternal. R' Yaakov points out that the word "omdim" is part of the tzivuy, the command of how to build the Mishkan. It's not a bracha -- it's something we have to make happen. So where do you get wood that will last for an eternity? The answer is you get wood that Avraham used for hachnasas orchim; you get wood that Yaakov invested his kochos in to prepare for the future and give his children bitachon that they would one day get out of galus and have a Mishkan. That's wood saturated with kedusha that will therefore be with us forever.
The world stands on three things: Torah, avodah, and chessed. Which of these values would you most associate with the Mishkan? The obvious choice is avodah = offering korbanos. The slightly less obvious choice is Torah. Ramban writes that the revelation of Shechina in the Mishkan parallels the revelation of Shechina at Har Sinai. The aron containing the luchos was the focal point of the Mishkan. Yet we see from the Targum Yonasan that the ingredient of chessed must be there as well. Only the wood that served as a vehicle for Avraham's welcoming of guests could serve to connect and hold that walls together.
My wife added that the Mishkan is a microcosm of the world. "Olam chessed yibaneh" - the world is built on chessed. The Mishkan follows suit.
The keruvin that stood atop the aron stood "pneihem ish el achiv" -- facing each other. R' Shternbruch suggests that the Torah is telling us that the key to being able to enter the kodesh kodashim, to be able to come close to the aron, to Torah, is to always look toward your fellow Jew -- to be aware of the needs and plight of your fellow man. Chessed is at the heart of the Mishkan.
What is true of the "house" of Hashem should be equally true of our own homes. Hashra'as haShechina requires avodah, requires Torah, but without chessed, it will all fall apart.