Security at Gillette is good. Fights are rare compared to before Kraft bought the team, there's an immediate "trouble" reporting system where people can text directly from their phones if/when something happens. Cameras are trained on every single seat as someone already mentioned. One possible problem is whether whoever has those seats sold them to Dolphins fans who can't be identified, although someone was taken into custody. The incident probably still is under investigation so it might be a bit before more info comes out.
One unique aspect to how season tickets are managed by the Patriots is ticket holders are responsible for someone behaving badly in their seats whoever it is. The penalty is losing future ticket privileges, a strong deterrent.