I have a Mini3 (1st gen, non-retina version) and I use it for chatting (mostly text), browsing and e-mailing, so sound/speaker quality is not important to me... but still, is there a way to improve the sound quality of the Mini3?

The speaker makes a crackling noise on some songs/sounds. You can try it yourself with the notification sound "Pollux" that is included in the recent versions of Android.