@etbaccata,

This has been an issue for a while, but we've been meaning to upgrade to HTML5 for a while and so fixing the old flash version has never been a really high priority.

For a workaround in the meantime, try right-clicking on the mp3 download link and selecting "Open in New Tab" (or new window). This should prompt the browser to open a new window and play the MP3 using its built-in MP3 player, which will usually provide more granulated seek functionality.