  The notion of weakly monotone functions extends the classical definition of
monotone function, that can be traced back to H.Lebesgue. It was introduced, in
the setting of Sobolev spaces, by J.Manfredi, and thoroughly investigated in
the more general framework of Orlicz-Sobolev spaces by diverse authors,
including T.Iwaniec, J.Kauhanen, P.Koskela, J.Maly, J.Onninen, X.Zhong. The
present paper complements and augments the available theory of pointwise
regularity properties of weakly monotone functions in Orlicz-Sobolev spaces. In
particular, a variant is proposed in a customary condition ensuring the
continuity of functions from these spaces which avoids a technical additional
assumption, and applies to certain situations when the latter is not fulfilled.
The continuity outside sets of zero Orlicz capacity, and outside sets of
(generalized) zero Hausdorff measure, will are also established when everywhere
continuity fails.
