I’m submitting this problem report to both OpenOffice and LibreOffice.

  To perform these steps, you will need to have Tahoma and Lucida Sans Unicode fonts (common) and EITHER Symbola font OR both FreeSerif font and Segoe UI Symbol font.  (While the latter are not as common, they are available for free).

1. The six test lines below all begin with a Unicode character followed by text which describes the character.  Copy the six lines into a WordPad document and change the font for the lines to Tahoma.  Note that only the Unicode character in the second line (sharp sign) is displayed.

2. Next change the font of all six lines to Lucida Sans Unicode.  Note that now the first two Unicode characters (flat and sharp) are displayed.

3. Now -either- change the last four lines to Symbola -or- change the middle two lines to FreeSerif and the last two lines to Segoe UI Symbol.  Note that now all the Unicode characters are displayed correctly.

  The first three steps have demonstrated the correct behavior.  I would expect the same behavior in OpenOffice Writer and LibreOffice Writer.

4. But now repeat the same three steps in either version of “Writer.”  Note that the Unicode characters in the last four lines are never displayed correctly.

5. Now change the last four lines to OpenSymbol font.  Note that this still doesn’t help...

It seems that this happens with any 5-hex-digit Unicode character which is supported by a font like Symbola, FreeSerif or Segoe Symbol UI in WordPad.  (Related LibreOffice Bug 71603 appears to be just one instance of this general problem with 5-hex-digit Unicode characters.)

I haven’t tried it in MS Word, but I’d assume that if it works in WordPad, it will work in Word.
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the six test lines:

♭  266D music flat sign
♯  266F music sharp sign