Hacking Netflix found this article, with photo, describing the process our movies go through at Netflix's Baton Rouge, Louisiana, distribution center, which opened September 1, 2004. The article says it's a typical DC, processing between 3,000 and 30,000 per day and employing eight people in an office setting, not a warehouse. According to Netflix's own fact sheet, the average DC processes 20,000 per day (3 million per day/30 distribution centers/5 days per week). They pick up their mail in the morning and drop it off in the afternoon after scanning it all in by hand.
If you have given your significant other a Netflix subscription for Valentine's Day, you may visit the link and read the rest of the story.