Hi Toby,
"Segments" are the XML container elements that associate a dimension and member to a fact in an instance document. The taxonomy's definition linkbase defines hypercubes (tables) and specifies which dimensions (axes) and members (points along an axis) are valid within them. So the definition linkbase defines what's valid, and the segment elements within contexts in the instance define what's actually applied to a fact. When these are out of sync, you get dimensional validation errors.
I'm simplifying a bit, but when dimensional validation runs, the concept and dimensions of each fact (as defined in segment or scenario elements) are checked against all hypercubes in the taxonomy. If the fact isn't dimensionally valid against any hypercube, a validation error is raised. Arelle won't tell you specifically which dimensions are missing or need to be removed because it doesn't know which hypercube you intended the fact to validate against.
What you need to do is identify which hypercube the concept is meant to be tagged against in the taxonomy. If the concept isn't modeled with any hypercubes (unlikely), then it shouldn't be tagged with dimensions at all. If it's modeled with multiple hypercubes, you'll need to determine which one applies to the fact you're trying to tag. Once you've identified the appropriate hypercube, you can use its defined dimensions as I outlined previously, using the arcroles from the dimensions tab.
Hope that helps clarify the model a little and doesn't just make it more confusing :)
Austin Matherne