The following simple batch file should do the job, if the .rtf files were originally created with Word or Wordpad. (Even though it's highly unlikely that it'll damage any of your files you may want to backup your Word documents before running it.)
Code:
FOR %%f IN ("*.doc") DO (
findstr /m /c:"rtf1" %%f && REN "%%f" "%%~nf.rtf"
)
Simply copy the above code to a text file, rename it to
word.cmd, copy it to the folder with the word files and double-click on it. (The batch file will automatically rename all .rtf files with a .doc extension to .rtf files.)
@eschwartz: findstr is the Windows equivalent of grep.