How to reduce Seq[Either[A,B]] to Either[A,Seq[B]]?

Edit: I missed that the title of your question asked for Either[Seq[A],Seq[B]], but I did read “I’d like to obtain the first error message or a concatenation of all error messages”, and this would give you the former:

def sequence[A, B](s: Seq[Either[A, B]]): Either[A, Seq[B]] =
  s.foldRight(Right(Nil): Either[A, List[B]]) {
    (e, acc) => for (xs <- acc.right; x <- e.right) yield x :: xs
  }

scala> sequence(List(Right(1), Right(2), Right(3)))
res2: Either[Nothing,Seq[Int]] = Right(List(1, 2, 3))

scala> sequence(List(Right(1), Left("error"), Right(3)))
res3: Either[java.lang.String,Seq[Int]] = Left(error)

Using Scalaz:

val xs: List[Either[String, Int]] = List(Right(1), Right(2), Right(3))

scala> xs.sequenceU
res0:  scala.util.Either[String,List[Int]] = Right(List(1, 2, 3))