Currently you can filter in RadMultiColumnComboBox only by setting the AutoFilter property.

Resolution: You can use the CompositeFilterDescriptors in RadMultiColumnComboBox and filter two or more columns. Please take a look at the code snippet: 
            this.radMultiColumnComboBox1.DisplayMember = "City";
            this.radMultiColumnComboBox1.AutoFilter = true;
            FilterDescriptor descriptor = new FilterDescriptor(this.radMultiColumnComboBox1.DisplayMember, FilterOperator.StartsWith, "Lo"); //first column
            FilterDescriptor descriptor2 = new FilterDescriptor("ContactName", FilterOperator.StartsWith, "Pe"); //second columns 
            CompositeFilterDescriptor compositeFilter = new CompositeFilterDescriptor();            
            compositeFilter.FilterDescriptors.Add(descriptor);
            compositeFilter.FilterDescriptors.Add(descriptor2);
            compositeFilter.LogicalOperator = FilterLogicalOperator.Or; //OR between these columns
            this.radMultiColumnComboBox1.EditorControl.FilterDescriptors.Add(compositeFilter);

Currently RadMultiColumnComboBox closes immediately when clicking on a  checkbox cell and does not allow changing its value.

Currently it is not possible to select multiple rows in RadMultiColumnComboBox.

Currently there is not support for simple binding for this property.

ADD. RadMultiColumnComboBox - add ability to display focus cues when DropDownStyle = DropDownList

RadMultiColumnComboBox should support suggest and suggest-append auto-complete modes when AutoFiltering is enabled.

Currently it is not possible to change the behavior of RadMultiColumnComboBox when using the AutoFilter mode. Check ticket ID 420127 for details.

This feature request refers to implementation of an AutoComplete mode for RadMultiColumnComboBox.

radMultiColumnComboBox €“ set AutoFilter to be true and apply filter to radMultiColumnComboBox. Apply the filter in this way so no result is displayed in the drop down. Try to open the drop down and you will see that you cannot.