Fisheyes are tiny crater or pock-like openings (like on a cheese pizza) that appear shortly after one sprays a coat of paint or primer over the intended area (primer is more forgiving and sometimes can be repaired by smoothing the afflicted area with deadened masking tape). Fisheye is caused primarily by spraying over a surface that's contaminated with oil, grease, or silicones found in car wax. To prevent fisheye you will need to use a pre-cleaner and possibly fisheye eliminator in the paint. If you end up with fisheye, there are a few ways to address the problem. First, you could let the area dry and then sand it to a smooth surface (below the fisheye craters) and respray the area. Or, if they show up in a basecoat, you can let the coat flash-dry and follow it with a real light mist coat to try and seal and bridge the fisheye. For really bad fisheyes you might want to grab a can of thinner or reducer and wash the entire area off, and start over.
Wrinkling, often called lifting, is when an existing paint layer shrivels during the application of a new finish or as the new finish dries. This is caused by the solvents in the new finish attacking the old finish. You'll most likely see this malady when recoating enamels or urethanes that are not fully cured, or if and when you exceed the maximum flash (dry) or recoat time during application. It'll also sometimes happen when you recoat a basecoat/clearcoat finish where the old clearcoat had an insufficient film build. In this situation, you'll have to strip and refinish. This circumstance can be prevented by not exceeding a product's maximum recoat time during or after application, by not shooting lacquer over enamel or urethane, or avoiding spraying under- or topcoats excessively wet.
Gas bubbles are similar in appearance to fisheyes (kind of like the difference between a roadster and a bubble top). These are caused by tiny gas bubbles trapped in the fresh paint film that rise to the surface and almost pop causing small, crater-like depressions. These are usually caused by under atomization of the paint due to either too low of an air pressure setting, improper spray gun adjustment, spraying with your gun too close to the surface, or moving your gun too slowly across a panel. Depending on its severity, gas bubbles can repaired by either sanding with 1,200-grit or finer paper and then polishing to restore gloss, or by sanding and respraying the area. You can avoid this problem by maintaining correct spray gun speed and distance, making sure you've got the right cap/nozzle/needle setup for the type of product you're spraying and making sure you're using the recommended air pressure.
Bleeding is when you end up with a discoloration in your topcoat color (most commonly a red or yellow stain) when painting over an existing finish. This is because the solvent in the fresh topcoat sometimes dissolves soluble pigments in the old finish, allowing them to seep upward into the fresh paint, thus discoloring it. You'll also sometimes see this when red crme hardener used in body filler bleeds up through a light color. You can sometimes repair a situation like this by letting the stained topcoat fully cure and then spraying a two-component sealer over it followed by a fresh coat of color. If you think you may encounter a possible bleeding situation your best bet would be to use a good sealer before the topcoat, or in the case of body filler under a light topcoat using white crme hardener instead of red or blue.
Die back, also known as dulling or hazing, is the dulling of a finish's gloss or shine as it dries or ages. This one is pretty common and has quite a few different causes. You'll be more susceptible to die back if you don't allow adequate drying or curing time of your undercoat, or if you close up a freshly painted vehicle in a spray booth or garage with no air circulation. The latter cause happens because in a sealed environment the evaporating solvents from the new finish hang around in the air and react with the still-drying paint surface, causing it to dull out. Other possible causes are to short a flash time between coats, using cheap off-brand thinners or reducers, and sometimes an excessively heavy and wet final coat. You can repair die back by letting the finish dry thoroughly and then cutting and buffing it or you can sand and refinish. You can also help to avoid the problem in the first place by applying your topcoats according to the product's directions, allowing sufficient flash times between coats, using the correct and/or recommended thinners or reducers, and making sure you've got good air flow around the vehicle as soon as its tack-free.