The Monolith puzzle. It confounded players for nearly a week after Fez was released, and ended up being solved by brute force. Surely after all the careful design and five years of development that were put into this game, this puzzle was not meant to be solved in such a way.
I have found a number of threads trying to unearth a solution, but nobody seems to have made any real headway. One would think that after three months, somebody would have figured it out by now. However, those few who have fully completed the game appear to have used the brute-forced solution (or been told said solution by a developer).
My hope is that someone somewhere has figured this out, but I fear that this question will remain unanswered.