I played morrowind once when I was younger - for around five minutes, but the awkwardness put me off. So I don't really know what kind of mysteries it has. I've played daggerfall, oblivion, and a little of skyrim (just got in a steam sale), and not really noticed an overarching mysteries.
One of the "mysteries" (more an overarching plot point) is that of the Towers, which was introduced in Oblivion (believe it or not) and fleshed out in Skyrim. Every game (except Arena) involves the destruction of a Tower by way of its Stone; the Mantella's destruction in Daggerfall lead to the fall of Walking-Brass (Numidium, the Brass Tower), Morrowind to the fall of Dagoth-Ur (Red Mountain, the Red Tower), Oblivion to White-Gold (White-Gold tower), and Skyrim to Snow-Throat (Throat of the World). These towers keep Mundus in existence; without the towers, the only thing keeping it around is Talos.
Another one is that of CHIM. CHIM is a fairly simple concept; one realizes that he or she is part of the dream of a Godhead and doesn't undergo an existential crisis leading to nonexistence ("zero-sum") in the process. CHIM is not a mystery in and of itself; its usage is known (even mentioned directly in Oblivion as the cause of the shift from jungle to uplands) and its nature is simple. What is far less simple is the concept of Amaranth, which is the step past. Amaranth is escaping the Godhead and dreaming your own dream. Tamriel itself is within the dream of Anu, whose ascendance is described in the Children's Anuad (him leaving time after fighting Padomay is where he began to dream; the rest after is conflating Anu the Amaranth with Anu who is Order). The identity of the Hidden Amaranth (Anu) was not known until about a month ago; there is one other Amaranth who will save the world from Landfall who may be revealed with C0DA in a few months.
Oh, yes, C0DA and Landfall. These are both the biggest mysteries of all, both stemming from but not quite directly from Morrowind. C0DA is apparently some sort of database that describes everything; at the same time, it is a graphic novel (~90 pages from what I last heard) by Michael Kirkbride describing Landfall, which should come out early 2014. Landfall is a total mystery; it involves the return of Numidium. There is a second sun in the sky at the time.
Also mysteries: the purpose of the Clockwork City, which not even Sotha Sil knew (will be answered in C0DA); where Yagrum Bagarn went after the Red Year (will be answered in C0DA); what exactly happened to the Dwemer (we know for a fact that they became the "skin" of Numidium, but what that entails is unknown); and how the Thalmor will succeed in their goal (KINMUNE founded the Thalmor apparently as an attempt to rid the world of humans; the existence of the second sun in
the Prophet of Landfall might be a hint as to their fate).