First, I'd like to say that both the pro and con side did very well considering how emotionally fueled the Trayvon Martin case has been, and how the case itself has become pretty large and pertinent, and because of that a lot of people have formed opinions without being fully informed.
I found the three strongest claims to be 1. Guns don't kill people, people kill people (Pro). 2. Stand Your Ground needs to be clarified, not restricted (Con). and 3. Under Stand Your Ground, immunity is defined too broadly (Con).
I thought that the pro's side strongest argument was that guns don't kill people, people kill people. Which, although has become sort of cliche, is 100% true and applicable. People need to be put under a certain kind of scrutiny, not gun laws.
However, I felt that by pointing this out, it almost negated their point, as Stand Your Ground law is a broadly defined law that states that a person is allowed to defend themselves; this argument was never about gun control, it was about the Stand Your Ground law, and effective it may or may not be.
Both sides made good arguments, but I felt the con side had more focus on the Stand Your Ground law itself. The law itself is very muddled, and because of that allows immunity to those who do not deserve it, and because of the muddled nature, those people do not even face public trial. I thought this piece of information best sums up the con sides argument, and I felt it a very persuasive argument.