If you bind the SelectedIndex or the SelectedItem properties to your ViewModel and change them from code, the UI will not be updated. This is both reproducible in ColorPicker, ColorSelector and ColorPaletteView. The issue is fixed in Q2 2014 Release.
You can't customize ButtonPart ot TogglePart of SplitButton in ColorPicker as SplitButtonStyle doesn't get applied with this property.
Implicit styles are set via refering included XAML files. Set Style targetting RadColorPicker and BasedOn RadColorPickerStyle. Set this stye in App.xaml after the resource dictionaries. In desinger - MS exception is thrown "This feature requires Microsoft.Windows.Design.Sevices.valueTranslationService". Note that this is only reproducible when xaml fiels are included in the project. This is NOT reproducible when you reference xaml files from the style dll (for example Telerik.Windows.Themes.Office_Black). The fix will be available in our official release Q2 2015 SP.