Good for you, writing from Jessie's perspective. I always thought I rather liked her better than most of the main female characters from the game. She just seemed more real.
In the third paragraph you're missing a part of your sentence: "On the surface, he was just another poor old man from the slums, leaning over the bar with the bottle of beer she'd . . ."
I like the way Jessie is frightened of the man but also reluctant to cause a scene or appear to be impolite. It's a very human reaction and it's easy to identify with.
You wrote all of the characters so well though and I really enjoyed the thought of Hojo being so contemptuous about the skills of the Turks that he had to set out looking for Aeris himself. Your descriptions of Hojo are excellent. I think what made the entire story so refreshing was that it was being seen from a new perspective.