How old is that radio? Do you have the manual and what does it say about being compatible with CD-R and -RW? -RWs have very characteristics when it comes to reflecting the reading laser. This may cause reading problems.
Also try doing a c1/c2-Scan of those discs with Plextools. It will give you a hint of burn-quality. What does Plextools say about the manufacturers of those discs (CD/DVD Info)? Is Mistubishi Chemicals the manufacturer? If yes those discs should work well @24x with your 716 (see link below).
Also how are you using those RWs? Are you always just ‘burning over’ the old content? If yes, try doing a full erase first and then burn the new content. That method has prooved to result in better quality. Look here for an example: http://club.cdfreaks.com/showpost.php?p=913452&postcount=2 and here for another one http://club.cdfreaks.com/showpost.php?p=984291&postcount=66