From Chrome's error console:
Uncaught Error: cannot call methods on slider prior to initialization; attempted to call method 'option' query.js:2
Safari's error console says the same (except it omits the word 'uncaught').
This started after I updated from WordPress 3.4.2 to 3.5 yesterday.
Safari 6.0.2, Chrome 23.0.1271.97, running in Mac OS 10.8.2 on a Mac Pro 8-core.
This error doesn't seem to occur in Firefox 17.01. It correlates with several problems - files not playing back, multiple songs being selected at once upon successive clicks, page jumping up to the top after clicking on a song, problems with time display, etc.
I tried the following, and the problems remained:
1. switched to the Twenty Twelve theme
2. disabled all other plugins
3. tried SCRIPT_DEBUG per these instructions in the Codex
Clearing the browser cache and then re-loading the page seems to resolve the issues in Safari, and then the player works as expected; but this doesn't seem to help in Chrome.
Test page is here.