I appreciate the Sherwin-Willaims Automotive Paint Troubleshooting Guide (PDF) for this. It is a very thorough guide that gives descriptions of what is going wrong, why, and how to avoid/fix it.
Here's a rundown of various problems with sample pictures of common names for problems. You can use the names as a starting point for further research. I'll be using the format of name (synonyms) [appearance time]
and where possible I've added links to relevant Mechanics.SE links to other questions related to those paint problems.
Air Trapping (Craters) [Rapidly during/after painting]
Bleeding (Discoloration) [Rapidly after painting]
Blistering (Pimples, bubbles, bumps) [Often weeks/months after application]
Blushing (Milkiness) [Rapidly during/after painting]
Chalking (Fading, oxidation, weathering) [Rapidly after painting/Naturally over time]
Chemical staining/etching (Spotting, acid rain, discoloration) [Happens due to chemicals on paint]
Chipping (nicks, stone pecks, chips, bruises) [Happens during driving]
Color Mismatch (Off shade, off color) [Noticed during/after painting/drying]
Cracking (Checking, Crazing, Spitting, Alligatoring, Crowsfeet) [can happen over long periods of time]
Dirt Contamination (dust in finish) [Rapidly during/after painting]
Edge Mapping (Edge ringing, featheredge lifting) [Rapidly after painting]
Fisheye (Silicone contamination, cratering) [Rapidly after painting, not later]
Loss of Gloss (Hazing, dulling, dieback, matting, weathering) [Rapidly after painting/Naturally over time]
Lifting (Wrinkling, raising, alligatoring, shriveling, swelling) [Rapidly after painting]
Mottling (Streaking, floating, flooding, tiger/zebra stripes) [Rapidly after painting, may not be immediately noticed]
Orange Peel (Poor flow, texture) [Rapidly after painting]
Peeling (Flaking, delamination, loss of adhesion) [Many causes, many times]
Pinholing (popping, bubbles, air pockets) [usually above body filler, rapidly during sanding]
Rail Dust (Rust specks) [Over time spots appear]
Sagging/Running (hangers, curtains, signatures) [Rapidly during/after painting]
Sanding Marks (Streaked finish, sand scratches) [After sanding]
Seediness (Gritty, Dirty, grainy, speckled) [Rapidly during painting]
I can't actually find a good picture of what this ends up looking like, likely because it's something that can be identified quickly while still painting. It happens when the paint material isn't working correctly, possibly due to age, lack of mixing or other contamination. It'll basically look like a metal speckled paint, but you weren't intending speckling to be there.
Shrinkage (Bullseyes, Ringing, Edge mapping) [Rapidly after painting]
Soft Film (Slow dry) [Paint is soft, will pick up finger prints. Rapidly after painting]
Solvent Popping (Boiling, blowing) [Weeks after painting]
Tape Tracking (tracks) [Upon tape removal]
Also can't find a good clear example of this. This is when the tape fails to properly separate colors due to using the wrong tape, or putting tape on a finish that isn't quite dry, leading to solvent hanging out and letting the next color bleed into the tape, then into the paint under the tape.
Transparency (Poor hiding, poor coverage, translucent, color bleed) [Rapidly after/during painting]
Water Spotting (Water Marking) [Rapidly after painting, or after washing]
Wrinlking (Crinkling, puckering, shriveling) [Rapidly during/after painting]