I ran into a scenario where the use of MonadError would only be valid if 
  catchError (pure a) h = pure a
was a law, so I looked up the laws in https://hackage.haskell.org/package/mtl-2.3/docs/Control-Monad-Error-Class.html#t:MonadError but surprisingly found none.

One would expect to see
  1. catchError (pure a) h = pure a
  2. catchError (throwError e) h = h e
  3. throwError e >>= f = throwError e

which would rule out silly instances like
  instance MonadError () Maybe where
    throwError ()        = Nothing
    catchError _ f = f ()

Searching for "monad error laws" gives me no haskell results, only https://typelevel.org/blog/2018/04/13/rethinking-monaderror.html which suggests the same laws.

I propose adding these 3 laws to MonadError haddocks.
AFAICT the IO/Maybe/Either/ExceptT instances in https://hackage.haskell.org/package/mtl-2.3/docs/src/Control.Monad.Error.Class.html%20 all obey the laws.