They need to start making truly pro-grade mirrorless cameras, with emphasis on functionality and ultimate capability rather than on small size/weight (same with the lenses).
Many of the foibles with mirrorless cameras now are because they're small, not because they're mirrorless - but, because of their price and full-frame status, they're competing against full-size SLRs. Compare them with miniature/small SLRs and you'll find that they, too, have a similar list of issues. The problem isn't one of technology, but one of will and market segmentation. For too long, they've sold mirrorless cameras as some sort of upgrade to a point-and-shoot, with emphasis on portability and small size, rather than as professional tools capable of replacing an SLR.