  We prove that no ultraproduct of Banach spaces via a countably incomplete
ultrafilter can contain $c_0$ complemented. This shows that a "result" widely
used in the theory of ultraproducts is wrong. We then amend a number of results
whose proofs had been infected by that statement. In particular we provide
proofs for the following statements: (i) All $M$-spaces, in particular all
$C(K)$-spaces, have ultrapowers isomorphic to ultrapowers of $c_0$, as well as
all their complemented subspaces isomorphic to their square. (ii) No ultrapower
of the Gurari\u \i\ space can be complemented in any $M$-space. (iii) There
exist Banach spaces not complemented in any $C(K)$-space having ultrapowers
isomorphic to a $C(K)$-space.
