Thanks the second one finally answered the question:

In summary, Gödel’s loophole is that the amendment procedures set forth in Article V self-apply to the constitutional statements in Article V themselves, including the entrenchment clauses in Article V. Furthermore, not only may Article V itself be amended, but it may also be amended in a downward direction (i.e., through an “anti-entrenchment” amendment making it easier to amend the Constitution). Lastly, the Gödelian problem of self-amendment or anti-entrenchment is unsolvable. In addition, the author identifies some “non-Gödelian” flaws or “design defects” in the Constitution and explains why most of these miscellaneous design defects are non-Gödelian or non-logical flaws.

I'm sad that there isn't an explanation of Godel's proof!

But, given that we can amend the constitution, it does seems fairly straightforward that a dictator could come to power, if there was approval of a super majority of the people.