Contrary to what some of you think - I believe that his off-the-field stuff will have an affect on where his is drafted. Character still does matter to an extent as NFL still worries a great deal about its perception. Ray Rice and Adrian Peterson are just two examples of backlash that teams have experienced, even though the "jury is still out" in Adrian's case. Someone will still draft Jameis in the first round of course, but I bet it will be later in the round when someone trades up to take him (similar to Manzell).
Remember that Winston off-the-field stuff is not limited to one episode. In less than two years he has been accused of sexual assault, allegedly been involved in one of those BB gun escapades, has signed over 2000 pieces of memorabilia (but claimed to have received no benefit - I have swampland for sale if you believe that) and been suspended for shouting something very vile while standing on a table in a school lunchroom. NFL also knows that the FSU community will look the other way in many instances when their football players are at risk, he will not have that luxury in most NFL cities.
And in a different way of sorts, look at Percy Harvin - he has some non-trivial character issues that have caused two teams to be happy to get what they could for him, even though he was one of the top players on the team. (although this may not be an issue with Winston, have not heard about any issues with teammates)