Optionally warn the user when an incorrect number is placed, or earmark is removed
I find that when I (attempt) to solve Sudokus quickly I sometimes makes mistakes that are not realized until later and which point they are not easy to fix - it's not clear where the mistake was made, just that the Sudoku is no longer solvable. When this happens I might give up. Given that I'm curious what optional feature could be added to warn me when I make the mistake.
Since QQWing, the Sudoku library used by GNOME Sudoku, can solve the Sudoku in milliseconds perhaps the solved Sudoku could be kept in memory. Each time a number is placed, or an earmark number is removed, if the solution is no longer possible the user is somehow informed. I'm not sure what the best way of informing the user would be, but putting something in the title bar would be easy to start with. Even if the user didn't notice it immediately the user could press undo until the title bar resumes displaying the usual "Sudoku".
Sudokus with multiple solutions are probably not worth supporting, at least to start with.
One corner case that is worth considering is guessing for hard puzzles. In that case the user shouldn't immediately be informed of the incorrect guess. Maybe the user could disable the feature prior to the guess to start with.
Incidentally, it would be nice if there was direct support for guessing, like it would set a save point that you could pop back to, and it would track which values had been tried. But that's out of scope for now.