Is the peak indicator supposed to be a peak level meter; ie show you when the sample from the cd hits digital full scale (0db)? If so, then I don't think there is anything wrong with it. If you are playing a relatively new rock/pop cd, I would expect the peak indicator to light constantly.
CDs today are mastered extremely hot (very high average power) and I have more than a few cds where the peak level meter constantly hits 0dB and clips (more than 3 consecutive samples at 0dB).