White Border around GroupBox

You could set BorderThickness to 0, but that would also hide the black border. The white color is part of the ControlTemplate, so you'll need to create a new template. Here is one I made by running the Reflector BamlViewer add-in on PresentationFramework.Aero and removing the two white borders:

<BorderGapMaskConverter x:Key="BorderGapMaskConverter"/><Style TargetType="{x:Type GroupBox}">    <Setter Property="BorderBrush" Value="#D5DFE5" />    <Setter Property="BorderThickness" Value="1" />    <Setter Property="Template">        <Setter.Value>            <ControlTemplate TargetType="{x:Type GroupBox}">                <Grid SnapsToDevicePixels="true">                    <Grid.ColumnDefinitions>                        <ColumnDefinition Width="6" />                        <ColumnDefinition Width="Auto" />                        <ColumnDefinition Width="*" />                        <ColumnDefinition Width="6" />                    </Grid.ColumnDefinitions>                    <Grid.RowDefinitions>                        <RowDefinition Height="Auto" />                        <RowDefinition Height="Auto" />                        <RowDefinition Height="*" />                        <RowDefinition Height="6" />                    </Grid.RowDefinitions>                    <Border CornerRadius="4" Grid.Row="1" Grid.RowSpan="3" Grid.Column="0" Grid.ColumnSpan="4" BorderThickness="{TemplateBinding BorderThickness}" BorderBrush="Transparent" Background="{TemplateBinding Background}" />                    <Border Name="Header" Padding="3,1,3,0" Grid.Row="0" Grid.RowSpan="2" Grid.Column="1">                        <ContentPresenter ContentSource="Header" RecognizesAccessKey="true" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" />                    </Border>                    <ContentPresenter Grid.Row="2" Grid.Column="1" Grid.ColumnSpan="2" Margin="{TemplateBinding Padding}" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" />                    <Border Grid.Row="1" Grid.RowSpan="3" Grid.ColumnSpan="4"  BorderThickness="{TemplateBinding BorderThickness}" BorderBrush="{TemplateBinding BorderBrush}" CornerRadius="3">                        <Border.OpacityMask>                            <MultiBinding Converter="{StaticResource BorderGapMaskConverter}" ConverterParameter="7">                                <Binding ElementName="Header" Path="ActualWidth" />                                <Binding Path="ActualWidth" RelativeSource="{RelativeSource Self}" />                                <Binding Path="ActualHeight" RelativeSource="{RelativeSource Self}" />                            </MultiBinding>                        </Border.OpacityMask>                    </Border>                </Grid>            </ControlTemplate>        </Setter.Value>    </Setter></Style>

You can try BorderThickness="0.5" if you are in a hurry.