I'm performing an incremental load into my cube (from a csv data source) but if some of the incremental data in my fact tables is associated with new dimension members, I'm not able to figure out how to also incrementally load new dimension related data. Is it possible to do this?
Yes it is possible. Similarly to the facts, dimensions can be incrementally loaded (see this page). You need to define the incremental load strategy that applies to the tables used to load the dimensions. In case you cannot ensure table consistency (facts rows are referencing existing dimension members), have a look to the unresolved rows policy (www).
Hope that helps.