I think it really depends on the individuals. A lot of the "don'ts" of the first date happened on my first date with the guy I'm with now, and yet it worked out perfectly fine. But that's because of the type of people we are.
The first date is mostly about first impressions and exchanging information. The second date is where chemistry really develops.
Get a bit more touchy, see where it goes. Try to do something active- I like to test out second dates with some kind of physical challenge so that you get a bit more physical and see if they have a competitive side. How a person competes shows you a lot about their character.