This is reproducible also with the Green theme. 

As a workaround you can extract the RadToolBar ControlTemplate and modify the column/row definitions of the root Grid element. 
(http://docs.telerik.com/devtools/wpf/styling-and-appearance/styling-apperance-editing-control-templates)

This is for vertical orientation:

<Grid.ColumnDefinitions>
	<ColumnDefinition x:Name="c0" Width="Auto"/>

<ColumnDefinition x:Name="c1" Width="*"/>
<ColumnDefinition x:Name="c2" Width="Auto"/>
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition x:Name="r0" Height="Auto"/>
<RowDefinition x:Name="r1" Height="*"/>
<RowDefinition x:Name="r2" Height="Auto"/>
</Grid.RowDefinitions>


This is for horizontal orientation:

<Grid.ColumnDefinitions>
<ColumnDefinition x:Name="c0" Width="Auto"/>
<ColumnDefinition x:Name="c1" Width="*"/>
<ColumnDefinition x:Name="c2" Width="Auto"/>
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition x:Name="r0" Height="*"/>
<RowDefinition x:Name="r1" Height="Auto"/>
<RowDefinition x:Name="r2" Height="Auto"/>
</Grid.RowDefinitions>

When the overflow button is clicked the OverflowPanel will be always open. Provide a support for closing the panel when the button is click again. 

Dear Support,

please add a property AutoCloseOverflowPanel (or similar) to RadToolBar that will cause the overflow panel to close automatically if the user moves the mouse outside of the overflow panel.

Rationale for this request: Consider a situation where RadComboBoxes or RadRibbonComboBoxes are used to modify the Font Familiy and the Font Size of text being entered. If the toolbar isn't given too much space, these controls will be placed on the overflow panel. If the user selects a new font and then wants to continue editing (using the new font)), at the moment he has to click somewhere outside the overflow panel. If he clicks inside the RadRichTextBox, he will most likely click in some area where he has already entered some text and the font family will be set to the font family of the text he clicked into.

For an example, please see my support request 1401504.

Kind Regards

Stephan Kühn

workaround:
for Material theme - add mat:MaterialAssist.FocusBrush = "{x:Null}" to the control instances you would like
for the rest of the themes: either set Focusable = "False" or retemplate and remove the focus in the StyleSelector of the RadToolbar

Allow navigation with the Up and Down keyboard keys in the overflow items when the popup is opened. The navigation should highlight the items and Enter press should activate them (the same that happens on item click).

This behavior is similar to the keyboard navigation in RadMenu and RadRibbonView.

The RadToolBar.OverflowMode attached property is not respected when set on an element in the ItemTemplate of RadToolBar.

When you are binding ItemSource to collection, the Height of RadToolbarTray becomes equals null so it's not visible.
Can you fix it please?

When the Orientation of the ToolBar is Vertical, in Windows8Touch theme the control is not sized properly. 

Available in LIB version: 2014.3.1326

The button focus visual should not be displayed when you click on another button in the UI. Currently, because the toolbar has its own focus scope, it is possible to have the focus on the button and also on another UI element. This means that the button will have its focus visual shown.

To work this around you can extract the Template of the RadButtonStyle from the Telerik.Windows.Themes.Fluent.xaml file and remove the General IsFoucused setters (MultiTrigger). Then you can apply the style using the style selector of the toolbar. For your convenience I prepared a small example showing this approach. I hope that helps.

https://docs.telerik.com/devtools/wpf/styling-and-appearance/styling-apperance-editing-control-templates

https://docs.telerik.com/devtools/wpf/controls/radtoolbar/styling-and-appearance/style-selector

When the RadToolBar is collapsed through the OverFlow Popup, the popup remains open. 

As a workaround the popup can be closed when the RadToolBar's Visibility is collapsed:

This is the most logged exception in my application and it looks like it's coming from RadToolBar: Specified element is already the logical child of another element. Disconnect it first.

Stacktrace:

The RadToolBar.ItemAlignment attached property is not respected when it is set to element inside DataTemplate.