Update: I've posted a solution to Deleting a Custom Member Property here
I've done this countless times; I've created my perfectly named Custom Member Property when it suddenly dawns on me that I've forgotten to give it the right data type. No problem, right? Wrong! From within PBM, can you change the data type? No! Can you delete the member property? No! Can you rename the member property? No!
So, what are the options? Well, you could wait for version 2 (I truly hope you can edit/delete member properties in V2!), you could hack the back end database in the vague hope of removing the member property safely, or, as I have been doing in the past, create a new member property with a less than perfect name and try not to clench teeth and fists every time I glance at the original.
Well, I've had enough, and decided I'm going to take action.
Strangely, the Microsoft.PerformancePoint.Planning.BMO assembly contains a method called DeleteDimensionAttribute on the Dimension attribute collection.