Minecraft – Where does the game store scoreboard information

The statistics are stored in your Minecraft data folder under stats, and Minecraft Wiki has some details on the format. We can see from the filenames (e.g. stats_kpreid_unsent.dat) that they are stored per-user. It does matter whether you are playing offline, because if you are offline it is as if you are playing the default username “Player” and so those statistics will be kept separately.

The statistics are collected across all worlds.

I agree that the statistics are screwy in some cases, but I don't have any specific info. Besides various obvious general flaws (e.g. counting all dyes as Ink Sacs), Minecraft thinks I've crafted more sugar than torches...

First off, they're stored client-side, so you can't restore players' waypoints on your side. They're in mods/rei_minimap in the minecraft folder. You should have a bunch of .points files in there.

Each file stores the waypoints for a single dimension in a world. Multiplayer waypoints are stored by server address, so if your server is on a consumer machine with a dynamic IP address, you should set up a hostname for it so players don't keep losing their waypoints.