Most paint by number advice tells you how to do it correctly. This is the other list: what to do once something has already gone wrong.
Nearly all of it is recoverable, and that is the useful thing to know before you start. Acrylic is opaque and it covers itself, so a mistake is a delay rather than a disaster.
The canvas arrived creased

If it arrived rolled, lay it flat and leave it an hour. It relaxes on its own.
If it arrived folded, the primer along the fold has cracked and the line will not fully disappear. Do not iron it directly. Tape the canvas flat to a board and leave it under even weight for a day, which softens the ridge, and accept that a trace will remain. Then buy from someone who ships in a tube next time. Ours do.
A pot of paint has thickened
Add water one drop at a time and stir it properly, working the stirrer around the bottom edge rather than swirling. Most thickened pots come back completely.
What not to do is tip in half a brush-load of water. Past roughly a quarter water you are diluting the binder as well as the pigment, and you get a film that dries chalky and will not cover the printed number.
A pot has dried solid
Water will not bring that back. Once acrylic has cured it is a plastic and it is no longer water-soluble, which is the whole reason it works as a paint.
The only real answer is a replacement. We keep a matching extra paint set for every design, which turns this from the end of the project into a short wait.
You have run out of a color
Almost always the sky, almost always at about eighty percent done. This is the most common reason a canvas ends up in a cupboard.
Two things reduce the chance of it happening: wipe the brush on the rim before each stroke so you are not laying paint on twice as thick as needed, and do the pale regions in two thin coats rather than one heavy one, which uses less paint overall and covers better.
You painted a region the wrong color
Let it dry completely, then paint the correct color straight over it. Two coats if the wrong color was darker than the right one.
Do not try to wipe it off while wet in the middle of a picture. You will lift the printed guide underneath and smear color into the neighboring regions, which turns one small problem into three.
Paint has gone somewhere it should not
Wet: a barely damp cloth, wiped once, gently.
Dry: paint over it with the correct color. Do not reach for rubbing alcohol, nail varnish remover or any solvent. They soften acrylic, and on a numbered canvas they will take the printed outline off with them.
You have smudged what you just painted
Let it dry, then repaint the smudged region. Then change the habit that caused it: work from the top of the canvas downward, work away from your painting hand rather than across it, and keep a sheet of clean paper under your wrist.
A region has no number printed in it
It happens on any printed canvas and it is usually a region carrying the same color as its neighbors. Check it against the full-color reference photo, look at what surrounds it, and use that. If you genuinely cannot tell, leave it until the areas around it are finished and the answer will be obvious.
The pale colors will not cover the numbers
They are not supposed to in one pass. Every region has black ink in it and pale acrylic has the least covering power of anything in the box. Let the first coat dry properly and go again. Two thin coats cover better than one thick one and leave no ridge.
The numbers are too small to read
Before blaming the kit, fix the light. An adjustable lamp coming over your shoulder from behind, rather than a ceiling light you are sitting under, solves more of this than anything else. Then use the printed reference sheet propped up beside you rather than hunting on the canvas, and keep a magnifier on the table for the finest sections.
For the next kit, buy the larger canvas size. The same design at 16x20 has the same number of regions spread over more area, so every number is bigger.
Your brush has splayed and will not hold a point
Usually because paint got up into the metal ferrule and dried there, forcing the bristles apart at the root. Once that has happened the brush is finished for detail work.
Prevention is the whole story: load the belly of the brush rather than pushing it in up to the metal, rinse in warm rather than hot water, never leave a brush standing in the water jar, and reshape the bristles to a point before drying. Our note on keeping small brushes precise covers it properly. A single good fine brush is the one purchase worth making.
The finished picture looks like a filled-in coloring book
This is the most common disappointment and it has one cause: stopping each color short of the printed line, which leaves a pale halo around every shape.
The fix works even after the fact. Look across the canvas at a shallow angle in good light and touch in every outline still visible, using whichever color it borders. It takes twenty minutes and it changes how the whole picture reads from across the room.
You have lost interest
Worth including because it is the most common failure of all, and it is not really a technique problem.
Leave it set up rather than packing it away, because a canvas that has to be unpacked gets painted far less often. Do thirty minutes rather than nothing. And if the design genuinely bores you, be honest about that too: the next one should be a picture you actually want to look at, not the one that seemed easiest.
For the working order that prevents most of the above, see the best way to do painting by numbers. For choosing the next design, how to choose a kit, and the designs themselves are in the full collection.