wow that Sucks.... I've washed my interior before... Please do this:
Get one of those wet carpet cleaner vacuums (try to find one with the Sofa attachment), and use it to shampoo/suck the water out. The shampoo will make the car smell nice and fresh, and the vacuum wil remove 90% of the water. DO NOT LET THE WATER SIT/EVAPORATE, by the time that happens you'll have guaranteed mold. And yes after shampooing/sucking all the water out, you will want to let the car air out, so leave the windows open while driving or while parked, and Please close the windows in the rain!
I have washed the interior of my windstar twice using this method, and it works extremely well.
NOTES:
1) It may smell musty if you leave the car closed up after you shampoo/vacuum the rugs (until all the water evaporates)
2) Try to avoid using the cleaning machines that have power brushes, especially on the edges of the floor mats (I'd take the floor mats out and wash out-of-car)
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1994 Ford Taurus LX 3.0L 156,000 miles
1998 Ford Windstar GL 3.8L 264,000 miles
2005 Toyota Prius Package 6 1.5L 158,000 miles
2006 Toyota Sienna LE 3.3L 45,000 miles
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