Hi Zac!
First of all, thanks for your interest in this project! I am very happy that after years, this robot is still being studied 🙂
To answer your question, indeed, in terms of load support, joint 2 is the one that has to support the most, followed by joint 3.
In terms of mechanical failures, the most sensitive parts and the ones that have ever broken are the gears that attach directly to the motor shaft. They are sensitive for two reasons, the first being temperature: Motors get hot during robot operation, and as the printed parts are in direct contact with the motor, they can reach temperatures high enough that they become malleable and deform due to the combination of stress and heat. That is why for all small parts that are in direct contact with the motors it is recommended to print them in ABS.
The second reason is the force that the gear teeth have to withstand. As they are small parts and are printed, due to the force they are supporting, if the layers are not well bonded to each other, they can break.
In the rest of the structure of the robot I have not observed mechanical failures of this type, but there is another that occurs in many axes and has to do with the flexibility of the assembly of the parts and their clearance. For example, the body of joint 2 (the one formed by the 8-shaped pieces and their intermediate connection) can be seen as an H if you look at it from the side. Because the connection of this body is only in the middle, when it is subjected to a lot of load the ends (especially the lower ones) tend to open up a bit. If this opening is large enough, the gears of the motors may not make good contact with the inside crown of the second joint, which can cause anything from a loss of steps of the motors to gear breakage.
Regarding the mechanics, these are the faults that I have detected the most, I hope it is of help!