I have looked around and thought a bit about what type of questions one (especially students) ask in journal clubs and I came up with the following list. It is not the most complete list and I am happy to hear suggestions about other things to have in mind. Also, it is prepared for students in the areas where engineering and applied mathematics meet, but can be applicable to other areas as well.

- What is the most important result of the discussed paper?
- Is the result incremental with well-understood foundations in the area? Is it new to the area but well-understood in another field of engineering/applied maths? Is it world shatteringly new? Or a waste of time?
- Was the paper clearly written? How was the flow of arguments? Were the variables defined properly? How was it structured?
- What is the most interesting aspect of the paper? It does not need to be the same as the most important bit above.
- What is the most fundamental mathematical concept mentioned and used?
- What can you say about computational aspects of the paper? For example, how does the proposed method scale? Or how does it perform in real time?
- How useful is the result? How realistic are the assumptions? How can you relax the assumptions?
- What would you do differently? How would you improve the paper?