As it is, what is currently and seemingly incomplete in M-theory? One example I can give is explaining dark matter proportions and.. how do we perceive the world as 4-dimensional.
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A major list of incomplete things in M-theory (I will ignore those that are not M-theory specific, which you can find in generic string theory questions):
I don't know if all of these are still active, or still unsolved, but these are the things that worry me when I think about M-theory personally. There is another thing that is not M-theory specific, but where I think M-theory methods are most promising:
One basic thing that's incomplete about M-Theory is that the theory isn't even completely defined. One can talk about M-Theory in certain limits where it reduces to string theory, or one can talk about the low energy (non-quantum) supergravity theory which M-Theory reduces to, but there is no definition of what M-Theory actually is as a quantum theory in 11 non-compact dimensions. In particular, the full quantum mechanical lagrangian for M2 branes is not known, although classical limits may be deduced.