The main advice is: just be careful. Read everything, twice if necessary. Do everything you are told to do and nothing you are not told to do. Follow the rules exactly. Then you'll be fine.
What happens if there were mid game events during the fist game. How are triggered them again during the second game?
In general, things which you open, stick on, write on or tear up are permanent changes. If they happen in the middle of your first game of a month, they'll be there from the beginning of your second game.
Any movable game components like cards and pawns and infection cubes get cleared up at the end of each game and reset at the start of the next.