The Validation.ErrorTemplate attached property is not set. To workaround this, you can use the following resource.

<ControlTemplate x:Key="ValidationTooltipTemplate">
    <Grid SnapsToDevicePixels="True" VerticalAlignment="Top">
        <Border Background="Transparent" HorizontalAlignment="Right" VerticalAlignment="Top" Width="3" Height="3"/>
        <AdornedElementPlaceholder x:Name="Holder"/>
        <Border BorderBrush="{StaticResource ValidationTooltipOuterBorder}" BorderThickness="1" CornerRadius="{StaticResource ValidationTooltip_CornerRadius}"/>
        <Path Data="M2,1 L6,1 6,5 Z" Fill="{StaticResource ValidationInnerTick}" Width="7" Height="7" HorizontalAlignment="Right" VerticalAlignment="Top"/>
        <Path Data="M0,0 L2,0 7,5 7,7 Z" Fill="{StaticResource ValidationOuterTick}" Width="7" Height="7" HorizontalAlignment="Right" VerticalAlignment="Top"/>
        <ToolTipService.ToolTip>
            <ToolTip x:Name="PART_ToolTip"
                DataContext="{Binding RelativeSource={RelativeSource Mode=Self}, Path=PlacementTarget.DataContext}"
                Template="{StaticResource ErrorTooltipTemplate}"
                Placement="Right"/>
        </ToolTipService.ToolTip>
    </Grid>
</ControlTemplate>

<Style TargetType="telerik:RadMultiColumnComboBox" BasedOn="{StaticResource RadMultiColumnComboBoxStyle}">
    <Setter Property="Validation.ErrorTemplate" Value="{StaticResource ValidationTooltipTemplate}" />
</Style>