There are a lot of Wiiware titles that are playable through the dolphin core, however, titles like Contra Rebirth or Castlevania the Adventure Rebirth crash upon starting the game after the title screen. This issue was resolved in standard dolphin by disabling the Dual Core but this function is not in the settings for the libretro core.
I had to end up using the stand alone emulator vs the core due to I couldnt get most games to load past the intros. I was told that the dolphin core needed some love in retro arch. However I never tried to do any wii ware titles in the core. Are you using the BIOS for the core? Also you might could find the setting the the config file for the core. I havent ever messed with config files directly in retroarch but it might be worth a try.
Edit: By the way I am not knocking retroarch by any means. I love retrosrch and it runs everything else I throw at it really well.