I, too, have water leakage problems with my 2000 Neon. Water gets behind the dash from somewhere (not windshield -- had it replaced) and finds a "basin" to collect in. Then, when taking a hard left turn on another day, the water can be heard swishing over to the passenger side and leaking out onto the floor.
I took the fan out, and found it rusted and binding. I cleaned, re-lubed, and replaced the fan. While its housing was removed, I looked for places water could get in by pouring water from the outside of the car, while a friend watched from inside -- nothing revealed. Dealer called it "a bad weld".
In New England winter, the water freezes around the fan, causing the fuse to blow whenever the fan is switched on... like automatically on defrost. Perfectly awful situation. Shame on Chrysler. REP.
I have a 1995 SOHC Dodge Neon.
In 2009 the rear main seal blew out requiring the removal of the engine (at 190 km). The rear main seal was made out of plastic and this is why the seal literally fell out. I pulled the engine myself and the seal was rubbing on the engine flex plate.
Then in 2010 the head gasket blew at the number 4 cylinder (at 210 km). I repaired the head gasket myself and it was a 5 day job (had the block and head resurfaced).
All in all, I think the Neon engine is fairly well designed, but it is obvious that some of the parts were not well designed, like the head gasket and rear main seal.
Check your rear headlights. This happened to me about two weeks after Sandy, and I came to find out my whole trunk and tire well was full of water. Take a cup of water and pour it around where your headlights are, and you will see if it drips. I ended up removing the carpet from my trunk and having it cleaned to prevent mold.