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.

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.

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--;
}

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

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

Change the TabItems layout when the TabControl OverflowMode="Wrap" with TabStripPlacement="Bottom" :
1. Let's say the wrap results in 3 lines. What we would expect is line 1 and 2 to be filling the entire width and line 3 to be partially filled. What we experience is line 1 partially filled and lines 2 and 3 filling the entire width 
2. When clicking on an item the lines swap around. The partially filled line can end up on top, in the middle or on the bottom. Clicking on items that cause tab rows to move up should re-flow the wrap.
3. Ideally - to look good - the logic should stretch the 'complete' rows to the entire width - i.e. it should adjust tab sizes to fill the entire width available on 'full' rows.

In the VS2010 designer the selected tab is the last one even if the SelectedIndex proeprty of the TabControl is set to 0. The issue can be reprodiced in a scenario where the RadTabControl is defined in a RadWindow control.

Using Xaml declared tab control with identical tab item headers will result in selecting the first occurance of selected text from the drop down content.
Add support for distinguishing different items in the drop down content (use DropDownDisplayMode=Visible) during selection and match to the corresponding TabItem.

Click event of a Button in the HeaderTemplate is not fired properly when another button outside the tab has IsDefault property set to true

SelectedItem does not respect the Reset collection changed action.