It would help to use RadWindow like System.Window with:
- WindowInteropHelper for correct modal behavior
- Set window in task bar, also set taskbar icon/title
- Use RadWindow as MainWindow in Application (set Application.MainWindow property with RadWindow 

Make it possible to add "No" button to the predefined RadWindow.Confirm dialog without the need of custom Template.

When a modal RadWindow is opened clicking out side of the Window (the overlay) should make a the Window blink and a sound should be played.

RadWindow.Confirm default button is OK, in order to change that presently we have to extract and modify styles, set FocusManager.FocusedElement binding to Cancel and set the ContentStyle property in code. 
It would be much more user friendly if this could be controlled by a simple property.

rendering problem is when minimized only

Available in the 2016 Q1 SP1 Release.

Maximizing RadWindow from the header button shows a window with the size of the content if SizeToContent = true. If you maximize with double click on header it is ok.

Make it possible to be able to drag the Window not only from its Header. In some cases it is useful to be able to drag the RadWindow from within its content.

When the attached TextOptions.TextFormattingMode="Display" property is set to the RadWindow the window stops auto resizing its size according to the size of its content.

As a user of the RadWindow control I want to be able to close it only by setting the DialogResult property without calling the Close method so that I can use it easily in MVVM scenarious.

The default Window control exposes an TaskbarItemInfo (https://msdn.microsoft.com/en-us/library/system.windows.window.taskbariteminfo%28v=vs.110%29.aspx?f=255&MSPPError=-2147217396) which is useful for manipulating the taskbar item of the Window instance.

It can be reproduced with the Show method of the window or with Dock, ToolWindows and the save - load functionality.

PreviewClosed event is called twice when using custom close button in DialogWindow

If a ContentControl is placed inside the control and the ResizeMode is set to NoResize the SizeToContent doesn't take effect.

As a workaround all you need to do is set the ResizeMode to NoResize in the Loaded event of the ContentControl.

Currently the template of the dialogs should be customized:
http://www.telerik.com/community/code-library/wpf/window/how-to-modify-the-alert-dialog-icon.aspx

Available in the 2016 Q1 Release: Added an IconTemplate property that provides an easier way to change the predefined dialogs' exclamation/question mark images.

As a workaround you can set:  window.CaptionHeight= 0;

When creating themed applications using RadControls, the standard Windows MessageBox control looks out of place.  With that in mind, the predefined RadWindows (Alert and Confirm) seem to be natural replacements for a typical MessageBox.  

However, when these dialogs open, they are silent  That is, they don't play any error, warning, or question sounds like the standard MessageBox - which makes them seem "strange" when used as a replacement.

Adding sounds to (for instance) the Alert window is fairly simple and can be accomplished like this:

RadWindow.Alert(new DialogParameters()
{
    Content = new System.Windows.Controls.TextBlock {
        Text = ex.Message, Width = 250, TextWrapping = TextWrapping.Wrap },
    Header = "Update Error",
    Opened = (alertDialog, eventArgs) => System.Media.SystemSounds.Exclamation.Play()
});

Though, it'd be nice if the ability to play a sound was built-in.  I'd suggest that the DialogParameters class used to customize the predefined dialogs be extended to support a SystemSound member of type System.Media.SystemSounds which, if defined, would play the specified sound when the dialog opens.