I agree with everything that's been said about it depending a lot on your ear (for music as well), age, and on opportunities to talk with native speakers. I also agree that an accent is usually not a problem unless it's so strong that it's distracting; and if that's the case, your ear may just not be very good.
But there's always room for improvement if you're motivated. If you really want to work on it, I suspect that Susi may be right to suggest making audio recordings of yourself and asking for feedback.
A group in the Spanish forum has exchanged links to audio clips that they post on commercial file-sharing sites: related discussion: Ton-LEO
. Caveat: Several people had trouble accessing the commercial sites or using the free software they downloaded, and I wouldn't really want to do that myself, for obvious reasons of privacy and security.
However, I noticed that LEO actually seems to have a option to upload audio files. I had to write this down, because it was so well hidden and not at all intuitive navigation for my taste, but I found it before atTrainer > Lerninhalte
(pop-down menu) > Übungen erstellen > Diktat > Neue Übung
(at lower right) > MP3-Datei hochladen
There was never any more interest in the Spanish group, so I didn't even try it myself. But if it did work, it might be possible to gather a study group of LEO users. If you wanted to try that, I might suggest posting links here, as some of us never visit the trainer section of LEO at all.
People with faster internet connections than I have seem to have had good experiences with internet phone services such as Skype, which are apparently not very expensive. If you could find a voice pal, analogous to a pen pal, in your target country, that might be another option worth exploring. If you posted under a registered nick with an envelope, other LEO users who were interested could contact you.