The hole is not in the middle
What happened. You went down where you were looking instead of where the clay was actually spinning. Your eyes sit off to one side of the wheel, so the visual center and the real center are never the same point.
Right now. If the walls are still thick, you can often save it. Slow the wheel, put a fingertip on the spinning surface to find the true dot, and open a second time from there, letting the new well swallow the old one. If the wall is already thin on one side, wire it off and start over. It is two minutes of clay and twenty minutes of frustration.
Next time. Find the still dot with a fingertip before you commit any pressure. Every time. It takes one second.
It went off center while I was pushing
What happened. Almost always unbraced arms, and almost always at speed. Your hand had nothing to push against except the clay, so the clay won. The second most common cause is pressing down and forward instead of straight down.
Right now. Do not chase it around the wheel. Lift off completely, slow down, re-anchor your elbows against your legs, find the dot again, and go back in gently. Chasing a wandering hole is how a good lump becomes a wobbling mess in about four seconds.
Next time. Elbows locked into your thighs before your hands touch anything, and open at roughly half the speed you centered at.
I went through the bottom
What happened. You did not stop early and you did not measure. That is the whole story, and everybody gets this one, usually more than once.
Right now. Wire it off and wedge it up. There is no honest patch for a hole in a wet floor. A plug of clay pressed into it will look fine on the wheel and will come apart at some point between the drying rack and the kiln, and you will not know which pot in the load is going to fail.
Next time. Tape on the needle tool, and treat step five as a rule instead of a suggestion. Stop shallow, measure, then go deeper if the number says you can.
The pot is short and it feels heavy
What happened. The clay never made it up. It is sitting in the floor, or in the inside corner, or in both, and no number of pulls will find it because pulls only move what is already in the wall.
Right now. If it is still wet, get a finger into the inside corner and drag that clay out and up before your next pull. That alone can add a surprising amount of height. If it is the floor that is too thick, trimming can take some of it back later, though you will be trimming a lot.
Next time. Clean the corner as step nine, every single time, before pull one.
There is a dome in the middle of the floor
What happened. You compressed from the outside toward the middle, or you widened by scooping, and clay piled up in the center. A dome is also what you get when the wheel head has a bump on it and you never noticed.
Right now. Flatten it with a rib, working center to corner, while the wheel turns slowly. Check it with the wheel stopped by laying a straight edge across it.
Next time. Every compression pass and every widening pass travels from the middle outward. Never the other way.
A crack appeared in the bottom weeks later
What happened. Almost certainly an S crack, and almost certainly no compression, or not enough of it. It shows up after drying or after the bisque firing, which is a cruel amount of delay between the mistake and the news.
Right now. Nothing. This is the honest answer and I am not going to dress it up. A fired S crack is not repairable in any way that produces a piece you would want to drink out of.
Next time. Compress after opening and again after widening. Also slow the drying down, because a floor stuck to a bat dries slower than a wall in open air, and that difference is what pulls the crack open.
There is a ridge or a lump in the inside corner
What happened. Your fingers rounded off before they reached the corner, so a wedge of clay got left standing in the valley. It is the most common thing a beginner cannot see, because you are looking down into a wet pot at the one spot the light does not reach.
Right now. Wheel turning slowly, finger pressed firmly into the corner, drag out and then up. You should feel the ridge give way. Sponge the water out first so you can actually feel what you are touching.
Next time. Make cleaning the corner its own deliberate step rather than something that happens on the way to something else.
The top tore open into a wide crater
What happened. Too much speed, too much sideways pressure, too early. The top of the lump is the least supported part of it, so it spreads first and it spreads fast.
Right now. If the crater is shallow, collar the top back in with both hands and carry on. If the rim is torn and ragged, cut it off level with a needle tool and accept a shorter pot.
Next time. Get your depth first, then widen. Trying to do both at once is what tears rims.
One side of the wall is thicker than the other
What happened. The well is off center even though the outside of the lump looks fine. This is the sneaky version of problem one, and it usually only announces itself when your first pull comes up thin on one side and fat on the other.
Right now. With thick walls you can sometimes re-center the inside by opening again from the true dot. Once the wall is thin, it is done. Wire it and move on with your evening.
Next time. After you open, rest a fingertip inside the well against the wall with the wheel spinning. An off center well beats against your finger once per rotation. You will feel it long before you can see it.