The control should allow customizations in its filtering functionality, for example, the developers should be able let RadComboBox match "Á" when the user types "A".

Place a RadComboBox control in a RadPane. Make it floating and dock it again. When selection is changed, the SelectionChanged event is fired multiple times.

Allow the developers to style the TextBox area of a editable RadComboBox - add icons, change the string, format the text etc.

It might also be nice to take it one step further and give the option to choose the key that fires an update off

When filtering is enabled, enter text that doesn't exist in the items and when the focus is removed the text entered is deleted, but it should stay.
The solution of this issue was implemented by a new feature in the control which determines if the Text of the RadComboBox should be updated on LostFocus or not.
Simply set the UpdateTextOnLostFocus dependency property of the control to "False". By default its value is True and no change in behavior should be observed.
The UpdateTextOnLostFocus dependency property is available in the 2015 Q2 SP1 release.

When the ComboBox is non editable.

Currently filtering with virtualized RadComboBox is not supported as the filtering feature works with the containers (changes their Visibility).

When the CheckBox is focused the issue is appearing.

Available in LIB version 2016.2.905, it will be also available in the 2016 R3 Release.

When IsEditable is set to true the SelectedItem is not updated if you delete the SelectedItem's text to match another existing item.

Available in the 2016 R3 Release.

Please check our help article for more information: 
http://docs.telerik.com/devtools/wpf/controls/radcombobox/features/multiple-selection

Place a RadComboBox in the GridViewColumn header and set SelectedIndex in the xaml. The SelectionChanged event is fired, but the command is not executed.

As a workaround you can set the SelectedIndex in xaml instead of on the Loaded event,

Currently the control scrolls by group.