Currently, if you have multiple tabs and the scrolling in the tabstirp area gets enabled, you can scroll using the mouse wheel. However, there is no behavior that handles the swipe gesture on touch devices (which is the alternative to the mouse wheel action). 
Add swipe scrolling support.

Pressing the Home and End keys selects the first/last items even if they are collapsed/hidden.

The scroll buttons are visible when the visible area is enough to display all tabs and the TabStripPlacement is set to Left/Right.

Introduce "Add new tab" button as in the RadTabbedWindow control which creates a new tab upon click.

When the window of an application that has a TabControl with Left/Right TabStripPlacement is resized, the measure of the TabStrip is incorrect and the ScrollButtons are in Disabled state. All Tabs should be visible when the window is in its normal state and should be scrollable.

RadTabControl is currently designed to support scrolling of RadTabItems only when any of them is currently focused. An ability to scroll RadTabItems without explicitly focusing them should be provided.

RadTabControlBase expose a protected method called OnPreviewSelectionChanged that should raise the event PreviewSelectionChanged event. This means that you should be able to override it and implement additional logic if necessary.

However, the method is never used in the code and therefore it is not fired when the PreviewSelectionChanged event raises. 

Use the method to raise the event.

The workaround is to set the IsContentPreserved of the RadTabControl to True.

By default, when selecting through the tab items, the first focusable element within each RadTabItem will gain focus. This is the behavior of the standard  RadTabItem as well. Provide an option to disable this default selection through a boolean property.

Workaround: Set HorizontalScrollBarVisibility property to Visible in order to show the scrollbar: 
<telerik:RadTabControl ScrollViewer.HorizontalScrollBarVisibility="Visible" .../>

or use Loaded event of TabControl and change the Height in order to trigger SizeChanged:
private void xTab_Loaded(object sender, RoutedEventArgs e)
{
    this.Height++;
    this.Height--;
}

In version 2016.2.613.45 of the Office2013 Theme, there is a problem in the control template for the RadTabControl. The ContentBorder element properly gets it's BorderThickness from the TemplatedParent, but the PlacementStates VisualStates override it with hard-coded Thickness (0,1,1,1 in the case of the "Left" Visual State) in their storyboards rather than doing an appropriate transform of the Thickness. This makes it impossible to override the BorderThickness for the control in any state other than the default layout without copying and replacing the entire control template. This appears to be a change in behavior since the (Februray 2016?) release, but I cannot be sure as the old theme files were uninstalled during the upgrade and the telerik.windows.controls.navigation.baml file is not properly decompiled in JustDecompile.

Selecting tabs with same names from the drop down menu always selects the first one.

Workaround:
Use the PreviewMouseLeftButtonUp and PreviewMouseLeftButtonDown events of the DropDownMenuItem. Handle the first event and invoke DropDownMenuItem.MouseLeftButtonUpEvent in the second in order to workaround the MouseLeftButtonUp event fired from the DropDownMenuButton and to call the logic for selecting the tabitem only when the dropdown menuitem is clicked (not just hovered). 

<Style TargetType="telerikTabControl:DropDownMenuItem">		
        <EventSetter Event="PreviewMouseLeftButtonUp" Handler="DropDownMenuItem_PreviewMouseLeftButtonUp" />
        <EventSetter Event="PreviewMouseLeftButtonDown" Handler="DropDownMenuItem_PreviewMouseLeftButtonDown" />
</Style>

private void DropDownMenuItem_PreviewMouseLeftButtonUp(object sender, MouseButtonEventArgs e)
{		
		e.Handled = true;
}

private void DropDownMenuItem_PreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
{
	var item = (sender as DropDownMenuItem);
	MouseButtonEventArgs mouseEventArgs = new MouseButtonEventArgs(Mouse.PrimaryDevice, 0, MouseButton.Left);
	mouseEventArgs.RoutedEvent = DropDownMenuItem.MouseLeftButtonUpEvent;
	item.RaiseEvent(mouseEventArgs);
}

When you have implicit DataTemplates applied to items the binding expression is lost on selection changed.

The SelectedTabContent is not added when the control is loaded in memory and a we try to create a ImageSource out of the UserControl hosting the TabControl

When a TabItem has a width (and the TabControl - don't) and if you try to resize the window so that the width of the window is less than the width of the TabItem - the TabItems start jumping

When a RadDocking is located inside a RadTabControl and the RadPaneGroup contains only one RadPane the content is scrolled(if located inside a ScrollViewer)

When the RadTabControl AllowDragReorder property is set to True and the control contains multiple rows with tabs, the dragging operation cannot be properly executed and completed.

SelectedItem does not respect the Reset collection changed action.