So how does the p2p trading part work exactly? Will there be folks in the meet up moving around with card boards stating how much Bitcoin they are selling or buying and the rates?
What happens in case of a dispute, since an escrow might not be involved?

I have an issue with physical meet ups, especially when buying and selling Bitcoins. It's the security of the assets. You don't know what kind of person you are meeting, they could be a robber or thief and by meeting them you are putting a bullseye on your back. You basically become a moving bank.
I had a friend get robbed similarly sometime back. They let him trade successfully, paid the money, but then later on trailed him and told him to give them back the funds on gun point.