What are some common mistakes students make with biochemistry?
The same as in any subject, that is, trying to memorise the material, instead of learning it and understanding it.
With any subject you study if you just memorise the material you're never really going to understand it. It is the difference between "shallow" learning and "deep" learning. You need to develop "deep" learning to fully master the subject.
The danger with memorising things is that they can become confused, whereas if you truly understand the material you are less likely to get confused and make mistakes.
When I was a student (many years ago) I tried to learn the Krebs cycle by memorising the different steps. It wasn't until I understood what was happening at each step, and why it was happening, that I fully appreciated and understood the cycle. Once I understood the cycle I found that I know longer needed to "remember" it.