Is there any way for Google Analytics to track multiple event parameters like Mixpanel?

While you can certainly make this work in Google Analytics, other analytics services like Mixpanel, KISSmetrics, Kontagent, etc specialize in event analysis and give you more flexibility. Having said that, you can hack the Google Analytics event model to get what you’re looking for.

If you want to track multiple parameters for each event in Google Analytics I’d suggest cramming the parameters you want to track into the event label. This is workable for two reasons: Event labels can be really long (ridiculously long, actually) and Google Analytics provides flexible filtering and segmentation options.

So, to extend an example discussed in an earlier answer, you could have an event for tracking video play details that looks like this:

_gaq.push(['_trackEvent', 'Videos', 'Play', 'title:MoreCatLolz, 
    percentPlayed:63, adShown:true, res:480p, fullScreen:false']);

All we've done is toss a few arbitrary parameters into the event label string in such a way that we can pull them out later. To analyze the results you could filter your event reports to show, say, the number of times the ‘MoreCatLolz’ video was shown with ads:

Alternately, using advanced segments and regex, you could count the number of visits in which users watched at least 90% of any video:

To track persistent user data, such as name, join date, level, purchase count, etc., I’d suggest using visitor-level custom variables which are automatically included with every tracking call (including events) and allow you to apply many of the same analysis techniques.