Using OOo 1.9.105 (WinXP) I create a new *.odt file and type in some paragraphs 
with german umlauts. Default font is Times Roman.
I select all and change the font to Arial, then I save the file as *.odt.

Now I save the file as *.rtf and open this file in MS Word2002.
The first paragraph is ok (font Arial), but in all other paragraphs the umlauts 
are shown in font Times Roman.

When I reopen the rtf-file in OOo, all the letters are back to Arial. Next save 
to *.rtf from OOo lets vanish the error.

Here you can see an extract of the rtf code of three in fact identical short 
paragraphs. The difference is shown in the change of \f3 to \f0 in the 
paragraphs 2-4 (but "normal letters" are shown in Arial):

{\fonttbl
{\f0\froman\fprq2\fcharset0 Times New Roman;}
{\f1\froman\fprq2\fcharset0 Times New Roman;}
{\f2\fnil\fprq2\fcharset0 Lucida Sans Unicode;}
{\f3\fswiss\fprq2\fcharset0 Arial;}
{\f4\fnil\fprq2\fcharset0 Tahoma;}
{\f5\fnil\fprq0\fcharset0 Tahoma;}}
...
     \pard\plain \ltrpar\s1\cf0{\*\hyphen2\hyphlead2\hyphtrail2\hyphmax0}
\aspalpha\ql\rtlch\af4\afs24\lang255\ltrch\dbch\af2\langfe255\hich\f3\fs24\lang1
031\loch\f3\fs24\lang1031 {\rtlch \ltrch\loch\f3\fs24\lang1031\i0\b0 Text:
Abcde\'c4\'dc\'d6\'df}
\par \pard\plain \ltrpar\s1\cf0{\*\hyphen2\hyphlead2\hyphtrail2\hyphmax0}
\aspalpha\ql\rtlch\af4\afs24\lang255\ltrch\dbch\af2\langfe255\hich\f0\fs24\lang1
031\loch\f0\fs24\lang1031 {\rtlch \ltrch\loch\f3\fs24\lang1031\i0\b0 Text:
Abcde\'c4\'dc\'d6\'df}
\par \pard\plain \ltrpar\s1\cf0{\*\hyphen2\hyphlead2\hyphtrail2\hyphmax0}
\aspalpha\ql\rtlch\af4\afs24\lang255\ltrch\dbch\af2\langfe255\hich\f0\fs24\lang1
031\loch\f0\fs24\lang1031 {\rtlch \ltrch\loch\f3\fs24\lang1031\i0\b0 Text:
Abcde\'c4\'dc\'d6\'df}
\par \pard\plain \ltrpar\s1\cf0{\*\hyphen2\hyphlead2\hyphtrail2\hyphmax0}
\aspalpha\ql\rtlch\af4\afs24\lang255\ltrch\dbch\af2\langfe255\hich\f0\fs24\lang1
031\loch\f0\fs24\lang1031 {\rtlch \ltrch\loch\f3\fs24\lang1031\i0\b0 Ende}