Monads should satisfy the "monad laws": left identity, right identity, and associativity.
IIRC, Haskell relies on two out of the three, but I don't remember which two. But if you write a "monad" that doesn't satisfy them (even though it has the right function signatures), then you're going to get bogus results.
Functor, monoid and monad laws allow for undefined evaluation order, lazy evaluation, parallell execution and same results for same parameters. But only if the laws holds can such be guaranteed when using certain abstractions. Associativity being one obvious caveat that might break abstraction over collections, while using divide & conquer mechanics such as function currying.
IIRC, Haskell relies on two out of the three, but I don't remember which two. But if you write a "monad" that doesn't satisfy them (even though it has the right function signatures), then you're going to get bogus results.