**gcc 4.5.2, Score: 8579.15** (or **14367.49** for filename "a.C", may update later)

Original file, 29 bytes, compiles clean (a.cpp):

    #if 0
    #include"a.cpp"
    #endif

Modified file, 30 bytes:

    #iff 0
    #include"a.cpp"
    #endif

Errors:

    $ gcc -c a.cpp 2>&1 | wc -c
    1286873

Score:

1286873 / (30 * 5) = 8579.15

Head and tail of error output:

    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0:
    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0,
                     from a.cpp:2:
    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:1:2: error: invalid preprocessing directive #iff
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2:

    ... And so on, backing out with second error after max include depth:

    a.cpp:3:2: error: #endif without #if
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:3:2: error: #endif without #if
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:3:2: error: #endif without #if
    In file included from a.cpp:2:0,
                     from a.cpp:2,
                     from a.cpp:2:
    a.cpp:3:2: error: #endif without #if
    In file included from a.cpp:2:0,
                     from a.cpp:2:
    a.cpp:3:2: error: #endif without #if
    In file included from a.cpp:2:0:
    a.cpp:3:2: error: #endif without #if
    a.cpp:3:2: error: #endif without #if

<sub>Note:<br>
- If `.C` ends up [qualifying as a valid extension](https://codegolf.stackexchange.com/questions/51659/1-character-typo-generating-most-error-messages-from-c-compilation/51671#comment122734_51659) then score is 1,206,869 / (28 * 3) = 14,367.49.<br>
- If Dennis' suggested second #include is added, file name "a.cpp", score is 80,797,292,934 / (46 * 5) = 351,292,578.97</sub>