Most pressing:

A graceful exit if a load fails (i.e., if the file being loaded wasn't
  generated by Denemo.)
Change all references to "mudela" to "lilypond", as has just been
  done for Lilypond.
Replacing the current ad-hoc mudela lexer with a flex lexer.
Bugfixing in cut, copy, and paste.
Add autoconf tests for getopt, errno.h.
If the existence of non-standard noteheads is remarked-upon in
  a Lilypond save file, Denemo will not reload that information.
  That needs to be fixed.
Fixing Makefile.am such that make dist works without a problem

Other stuff:

An option for entering note durations Lilypond-style rather than
  what's used now.
Automatic printing command.
Multinote slurs.
Common and cut time options.
"Clone" and "linkage" effects for tied notes.
Lyrics
Ability to enter MIDI patch numbers rather than instrument names
  in score properties, ability to select from a list of instrument names,
  etc. To do this I'll need a data file and a quark relating patch numbers
  to instrument names & vice-versa.
Using a point-and-click keyboard widget, in part as a preparation for
  note entry via MIDI keyboard. I'll probably use the one
  included with Smurf.
Reformatting code for greater compliance with the GNU coding standards.
  This is coming along well in terms of whitespace formatting thanks
  to GNU indent, but s still need to be inserted in sensible
  places, variable and function names need to be rewritten with
  underscores_separating_words, and so on.
Support for undo. (either with GUndo or rolling it myself.)
Making it so that accidentals on the same chord to no longer collide with
  each other.
Renewed support for multiple simultaneous time signatures
Intelligent drawing mechanisms that don't repaint the whole drawing area
  with each keypress, if possible
More menubar commands
More mass operations to selected regions (clear, single-bar move,
  transposition, etc.)
Rework Denemo so that it can open multiple files at once (shouldn't actually
  be too hard)
FILTER_MASK is invoked only where it presently needs to be. It should be
  used more gratuitously for better maintainability.

And, long-term TODOs:

MIDI keyboard note entry support
Internationalization