Can a subgroup of a public group be private and hidden?
I recently experienced this same "Undefined index: field_mode in OgBehaviorHandler..." error when trying to set the og_group_ref field widget to select list. It appears that it doesn't work if it's not set to "OG Reference". In the "Additional behaviors" field, you can set it to select there, but the widget needs to be left as the default value. Try that and see if it's of any help.