Drew,
Hang on - I agree with Heath and Nicholma about finger oils and fish eyes, but if there are "cracks" appearing in waterbased acrylic paint (especially Tamiya acrylic paint), then I'll wager my house on the problem being the undercoat and the topcoat are drying at different rates, causing the top coat to crack as the undercoat shrinks.
I've had this happen a number of times, especially with Tamiya acrylics. Having said that, I still use Tamiya paints quite often, and recommend them. You just have to modify the way you apply them.
As the above two posts tell you, carefully wash the parts with detergent and allow to air dry. I always sand car bodies with 600-800 wet-or-dry to give the surface "tooth" or something for the paint to grab onto.
I apply a thin coat of primer and allow to dry thoroughly - a day or two is usually enough for primers. I usually use an enamel primer, or (even better) an automotive acrylic - but you have to be careful as the thinner in auto acrylic is "hot" and can soften styrene in large doses.
Applying the acrylic top coat should take time - apply a couple of THIN mist coats at first, wait a little, then nail it with a wet coat. Applying these three or four coats before the paint is completely dry allows all the coats to set-up (mingle with each other) and dry as a single coat. If you spray a wet coat, let it dry, then hit it with another wet coat, the thinner in the new coat attacks the paint in the first coat, causing it to expand and contract a little - which can cause cracks as they both dry (again, at different rates).
Sorry for the long winded post, but give it a try. You should be able to get perfect results with Tamiya paints - just experiment a little.