What are some common mistakes students make with boat and chair conformations?
I have said this before, but the biggest mistake you can make is NOT to use a set of models.
In an exam you have to depict on two dimensional paper, a three dimensional molecule. This is not a trivial issue. If you make a model , you have the three-dimensional structure for reference, and most models are robust enough to allow the easy transformation of a chair to a twist-boat to a boat to the other chair conformation.
A model shows you how axial substituents become equatorial and vice versa. You still have to be able to represent your model on the two-dimensional page. But please do not be embarrassed if you have to use a model to visualize something. On the desks of very distinguished professors of organic chemistry you would always find a set of models, and with which the prof would always be fiddling.