Best guess would be the door isn't sealing properly. I've had my hinges wear and the door sag. I've also had the body tweak a little and had the door sag.
Sometimes if you get just the right angle, while sitting in the drivers seat you can see light around the door seal.
I occasionally use a dollar bill, close the door on the dollar bill (in various spots) and see how easy it comes out from between the the door seal and the door. It should have a little resistance when you pull it out, if it is making a good seal.
My method for getting the door back up again where it is supposed to be, is rather crude but effective. I use a foot long piece of 2X4 wood put it under the door with it partially opened and use a screw jack or bottle jack to jack the door up (near the end to get as much levarge as possible and lessen the probabilty of bending the door bottom). I kind of do it in stages, so I don't overdo it. Kind of a trial and error type thing. The door seal is just glued on there and really not that big a deal to replace, the type and size is used in numerous other models and not that hard to find (it's not jeep specific).
The hinges are know to tear the sheet metal they are welded to, worth a look.
There was a TSB out way back when (I guess), my dealer installed some extra rubber, shaped like a windshield wiper blade, but with mounts and screw tabs. My guess is to channel the ran water away from trouble spots. My door never really leaked much, my guess is they did it as a preventative measure.
Word of warning, leaving that water down there and/or the carpet and pad staying wet or moist all the time, can rot the floor out. It will also rot the splices for some of the wiring running under the carpet and can cause battery leak down problems.
You may want to loosen the door latch catch, the knob looking thing the door latch/locking mechanism grabs and move it inwards a little. I mark it before I start, loosen it a little and then tap it with a hammer. If you loosen it too much, the knob (catch), can move more than you'd think, that's why I mark a ring around the base with a marker before I start (as a reference point).
