To reproduce: try to hide the caret: 
this.radRichTextEditor1.CaretWidth = 0;

Workaround:

//Flow layout
this.radRichTextEditor1.LayoutMode = DocumentLayoutMode.Flow;
Telerik.WinControls.RichTextEditor.UI.DocumentWebLayoutPresenter webLayoutPresenter =
    this.radRichTextEditor1.RichTextBoxElement.ActiveEditorPresenter as Telerik.WinControls.RichTextEditor.UI.DocumentWebLayoutPresenter;
webLayoutPresenter.Caret.Width = 0;

//Page layout
this.radRichTextEditor1.LayoutMode = DocumentLayoutMode.Paged;
Telerik.WinControls.RichTextEditor.UI.DocumentPrintLayoutPresenter activeEditorPresenter1 = 
    this.radRichTextEditor1.RichTextBoxElement.ActiveEditorPresenter as DocumentPrintLayoutPresenter;
activeEditorPresenter1.Caret.Width = 0;