I've ran into this by modifying the samples for attribute editing to match my development environment.
The geometry of my feature do have m values.
The geometry editing works great, but any attribute editing will not stick, I receive the following error:
{"addResults":[],"updateResults":[{"objectId":398,"globalId" : null,"success":false,"error":{"code":-2147221399,"description":"Geometry does not have M Value(s), hence cannot update the feature."}}],"deleteResults":[]}
I am assuming you mean geometry edits of New Polyline features. According to ESRI there are limitations with Web Editing of polyline features that are m-aware. You can create and delete polylines that are m-aware but you can not update existing features that are m-aware.
Test this by creating a new polyline feature class that is not m-aware. Please respond with your results.
