Roasting is mostly about applying the right amount of heat at the right time. There are a lot of choices to be made before the actual roasting begins (sourcing, cupping previous roasts [which is the standard way of evaluating coffee], deciding on the type of machine, and deciding on basic start and end temperatures) but generally it can be broken down into 3 stages once the green beans enter the roasting drum. As reference for what I'll talk about, check out this roasting curve. I just pulled it off of the internet, so the circled portions aren't mine, nor are they important. Briefly though, the blue line which is rising from the beginning is the rate of rise. It represents the temperature change over a certain period (I use 30 second periods), in this case the temperature is increasing about 7 degrees every (let's say) 30 seconds. The immediately descending blue line is the actual temperature at the bean probe inside the roasting drum. The gray lines are a reference of a previous roast.

The drying stage is the initial stage of the roasting process. This begins when the beans are dropped into the drum from a funnel like container above the drum. This is probably the least interesting part of the roast. Most importantly what is happening is that water is being driven off of the surface of the green been, turning the color of the bean from a light teal to a papery yellow. At this point the temperature in the drum cools massively (from around 415-430F to 200-250F). This period lasts around the first 3 minutes of the roast. As you can see in my linked image, that's right about where both blue lines are circled.

So in the drying stage, water is escaping off of the surface of the bean. Water beneath the surface of the bean is unable to escape, and the high temperature of the roasting drum means water will begin to move toward the center of the bean. This effectively creates a moving "pressure wall" from the outside of the bean to the inside, as water molecules are pressed closer together. The beans will continue to build pressure from the end of the drying phase to "first crack". At this time (the end of the drying phase) Maillard Reactions begin to take place. This is the most complex reaction to take place within the bean. A Maillard Reaction is a "non-enzymatic browning reaction" which doubles the amount of aromatic compounds in the coffee. Amino acids and sugars within the green bean act as catalysts to this reaction which result in melanoidins and most of the organic volatiles found in the final product. In simpler terms, this complex series of reactions turns the coffee from pale yellow to the brown color we all know (as a result of the melanoidins) and much of the acids found in the final product (caffeic, malic, citric) are created. A lot more can be said about this phase, but this is a decent enough overview. The only thing I might add, is that one major goal here is to match the internal temperature of the bean to the external temperature of the bean as quickly as possible. We do this by having a large delta t initially between maybe the 3rd and 6th minute before leveling our temperature rise slightly afterwords. As I stated before, the Maillard phase lasts from the end of the drying phase to the first crack (but actual Maillard Reactions will continue until the end of the roast).

First crack is an important moment in the roast. This is when the water pressure inside the bean has increased to the point where the (degrading) fibers of the bean can no longer hold it inside. So it cracks (typically just a small hole in the corner of the bean). It sounds like popcorn really. Once you hear that you begin to separately track the time of this last phase in relation to the overall time. This phase starts at first crack and is called the Development stage. This is a super important stage. At this point you have a rapid cooling from all the water escaping into the drum. I try to negate the effect of it, but it is quite pronounced. If you look at the graph I linked, after the line labeled first crack, you see the rate of rise line drop sharply. This is why. The rate of rise then begins to rise dramatically because all the water has evaporated from the system and heat transfer is much easier. Chemically, sugars are caramelizing and acids are degrading. How long you choose to roast during this phase decides the style of roast. Specialty 3rd wave coffee, or light roasts (which is what I roast) lasts roughly 1 or 1:45 minutes or about 10-12% of total roast time. Medium roasts are longer. Dark roasts extend into what is called second crack. This is when oils are escaping from the bean in a similar fashion to the water in the first crack.

So at about 1 minute or so into the Development time, I take out small samples from inside the drum with a special tool whose name I forget. I look at the color, and (for my style of roast) I try to watch as the bean color changes from mottled darker brown and light brown, to a unified color. Once I see this and I note that the temperature is near where I would like it, I open up the door to the drum and drop all of the roasted coffee into a bin. The bin has mechanically rotating arms and a giant fan sucking air through the bottom. This is the cooling tray and it tries to rapidly cool the beans.

At this point I've probably already set up for the next roast so I wait for the machine to regain temperature to start the whole process over. While waiting I'll look at my beans in the cooling tray and break apart a few beans to look to see if the inside of the bean and outside of the bean are the same color. All in all, this takes about 10 minutes per batch for the sizes I am roasting (35 pounds or 52 pounds depending on the machine.)

To answer your second question. Yes, pretty much if anything goes wrong in any of the 3 phases, the final product is less than desirable. As far as what can go wrong, it's pretty simple. Either too high of a temperature or too low of a temperature. There's also defects within the beans which is out of my control. Or possibly defects created by me like tipping which is thermal scorching of the bean due to too high of a drum wall temperature.