So far I've found two sources that, if gaining from them puts you over 9999 POINTs, lowers it down to 9999 (also occurs if you already had over 9999 and gained more.) These two sources include the chest in the watercooler room in TV World, the one behind the fake red spikes. The second location is the game puzzle beyond the second cowboy game, where you need to throw bridge pieces to cross the water. The chest you're "rewarded" for beating this puzzle will knock you back down to 9999 POINTs.
Edit: The chest beyond the Zapper at the end of TV World (on the boardwalk, below the Shuttah) gives you one point, and also lowers your POINTs to 9999.
