Using the mouse, placing the visible cursor between two supplementary characters in a JTextArea or JTextField can break up the supplementary character pair of code units. The result is that user can insert new characters between code units that should never be separated.

The misplaced document dot/mark occurs only when the visible cursor touches the trailing part of a supplementary character glyph in a sequence of multiple supplementary characters. Suspect a viewToModel(x,y) problem...