I've been using W3 Total Cache for months (years really) on all types of websites. It has usually done the job extremely well.
Unfortunately, there is a problem between version 0.9.3 and wordpress 3.8.1. The plug-in conflicts with WordPress and the result is 500 errors coming up every few minutes (or seconds). This conflict isn't a problem on websites with small traffic as it doesn't seem that things build up enough to cause the disruption but it causes hell on large traffic websites (the ones it's use is crucial).
According to my observations on 20 or so websites using the plugin, there seems to be a strong correlation between the traffic and the rhythm the errors occur. I didn't see any error on websites with up to 150 visitors per day.
So if your overall daily traffic is average & under 100 visitors, you're probably safe using this plug-in before an update fixing the problem is launched. If your website is popular, stay free from W3 Total Cache for the moment.