I used to do maintenance on a in-house system that had originally been developed by some consultants (I used to not like consultants as a result of that). Parts of it were reasonably well written and other parts were really, really ugly.

While there were a few cases where entire chunks of the app got ripped/replaced as they were too horribly broken to be fixed incrementally, my approach was mostly to fix *only* the piece that needed to changing (that piece, that whole piece, and mostly nothing but that piece). FWIW, I considered a piece to be a function, subroutine, and/or method.

For that piece,

1. First I'd fix the indenting/whitespace.

2. Then I'd pick a variable, figure out a better name and rename it-- I tended to search/replace one by one and checked how the variable was being used as I went. It was amazing how much dead code there was in the form of

   declare $variable...
   set $variable...
   set $variable again...
   set $variable yet again...
   end of code piece-- value of $variable never used.

3. Repeated step 2 for all variables, removing dead sections and unused variables as they were found.

4. Ensured that the code still worked the same as before I started.

5. Refactored the piece if it made sense to do so.

6. Tested it again.

7. Made my change.

8. Tested it again.

Using this approach, I never rewrote the whole thing application, just the pieces that needed changes whether those changes were for bug fixes or new/different functionality.

Some observations that I made alng the way was that there tended to be a correlation between:
1. formatting and code quality (poor formatting ~ poor quality),
2. global variable useage and code quality (lot's of globals used ~ poor quality), and
3. unused variables and code quality (lot's of unused variables ~ poor quality).

my 2 cents.

The box said "Requires Windows 98 or better" so I installed Linux.