To reproduce:
 public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();

            Random r = new Random();
            DataTable table = new DataTable();
            table.Columns.Add("ID", typeof(int));
            table.Columns.Add("Name", typeof(string));

            for (int i = 0; i < 10; i++)
            {
                table.Rows.Add(i, "Row with longer value " + i);
            }

            radMultiColumnComboBox1.DropDownOpening += radMultiColumnComboBox1_DropDownOpening;
            radMultiColumnComboBox1.AutoSizeDropDownToBestFit = true;
            radMultiColumnComboBox1.DataSource = table;
        }

        void radMultiColumnComboBox1_DropDownOpening(object sender, CancelEventArgs args)
        {
         //  radMultiColumnComboBox1.BestFitColumns();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            Random r = new Random();
            DataTable table = new DataTable();
            table.Columns.Add("ID", typeof(int));
            table.Columns.Add("Name", typeof(string));

            for (int i = 0; i < 10; i++)
            {
                table.Rows.Add(i, "Row " + i);
            }

            radMultiColumnComboBox1.DataSource = table;

        }
    }

WORKAROUND: call the BestFitColumns method in the DropDownOpening event

Steps to reproduce:
1) Add RadGridView control
2) Add GridViewMultiComboBoxColumn column:

            GridViewMultiComboBoxColumn multiCoomboBoxColumn = new GridViewMultiComboBoxColumn();
            multiCoomboBoxColumn.DataSource = customTable;
        

Workaround:
do not set the DropDownHeight 
property. Instead, you could set the AutoSizeDropDownToBestFit property to true and the MaxDropDownItems property, which gets or sets the maximum number of items to be shown in the drop-down portion. Here is a sample code snippet:
RadMultiColumnComboBoxElement element = e.ActiveEditor as RadMultiColumnComboBoxElement;
element.AutoSizeDropDownToBestFit = true;
element.MaxDropDownItems = 20;

When set the SelectedIndex property in the DropDownClosed event selected index is not set correctly.  

Workaround:
private void radMultiColumnComboBox1_DropDownClosed(object sender, Telerik.WinControls.UI.RadPopupClosedEventArgs args) 

{

this.radMultiColumnComboBox1.SelectedIndex = 0; 

this.radMultiColumnComboBox1.EditorControl.CurrentRowChanging += new CurrentRowChangingEventHandler(EditorControl_CurrentRowChanging); 

}

void EditorControl_CurrentRowChanging(object sender, CurrentRowChangingEventArgs e) 

{

e.Cancel = true; 

this.radMultiColumnComboBox1.EditorControl.CurrentRowChanging -= EditorControl_CurrentRowChanging; 

} 

When filtering is applied to RadMultiColumnComboBox editor in CellEditorInitialized event of RadGridView, the selected item is second one, if the new row is edited.

Workaround: change the event handler by adding the following lines of code in the end of the RadGridView1_CellEditorInitialized:

Dim value As Object = e.Row.Cells(e.ColumnIndex).Value
 
If value Is Nothing Then
    editor.EditorControl.CurrentRow = Nothing
Else
    editor.Value = e.Row.Cells(e.ColumnIndex).Value
End If

Workaround:

radMultiColumnComboBox1.DropDownOpening += new RadPopupOpeningEventHandler(radMultiColumnComboBox1_DropDownOpening);
....
 void radMultiColumnComboBox1_DropDownOpening(object sender, CancelEventArgs args)
        {
            int width = 0;
            foreach (GridViewDataColumn col in radMultiColumnComboBox1.EditorControl.Columns)
            {
                width += col.Width;
            }
            radMultiColumnComboBox1.MultiColumnComboBoxElement.MultiColumnPopupForm.MinimumSize = new Size(width, 0);
             
        }

1. Create a new project and add RadMultiColumnComboBox
2. Bind it and setup filtering
3. Attach to SelectedValueChanged and SelectedIndexChanged events
4. Run the project
5. Apply some filtering and you will see that these events will not fire, regardless that the current row has changed.

Work around it by using the EditorControl.CurrentRowChanged event instead of SelectedValueChanged/SelectedIndexChanged events.