Is the SSIS package configured to ignore errors, or is the error handling of the cube itself configured to ignore them?

I've found that changing the error handling of dimensions to default and then custom, followed by careful examination of the settings there can help a lot.

Are you processing dimensions, then measures, then the cube as a whole in that order? I've found that you have to process dimensions first to get them up to speed before you process the data or you can get those kinds of errors too.