My idea for the chat is to have a limit for how many posts are remembered by the game. Limiting how many posts you can scroll through would allow everyone to actually scroll through everything without several posts at a time not being seen due to the overload of just how many there are.
I just ran into this issue earlier today while roleplaying- a few different people posted at the same time, long posts, and it was incredibly difficult to see what the first one said, due to it being skipped to one from before that. Not only are entire posts skipped once the game has been open for a while with posts continuing to come in, but a sentence or two within a single post ends up being incapable of being seen until more people post, moving that specific one into just the right position to actually see all of it.
If you want to have the game remember absolutely everything said, then limit the amount of posts the current chat window can have on it, adding a "see older chats" option at the top that can open a new window that shows everything that has been said.
Or, if the amount of posts isn't the issue, possibly edit the scrollbar to be easier to use. For example, like the one this forum and typically all of the internet uses - it gets smaller as there is more to see, and slides fluidly instead of in the a block-like fashion that the game currently has.