The stochastic discount factor $M_t$ in a simple RBC model
Somewhat inconsistent/careless use of indices. In 

$$M_t=\beta^t\frac{E_0(u'(C_{t+1}))}{u'(C_{0}))}$$

it is assumed that we stand at period $0$ for any $t$ ahead we want to look at.

In 

$$E_t(M_{t+1})=\beta\frac{E_t(u'(C_{t+1}))}{u'(C_{t}))}$$

it is assumed that we stand at any $t$ and we look one period ahead.

The two expressions don't give the same formulae for any given $t$, and there lies the problem/confusion.