I am an instructor teaching a remote class that holds some discussion sections in person and some discussion sections remotely. How should I deliver exams?

In general, your starting point should be to hold the exams in the same format in which most students are receiving instruction. This is not a requirement for faculty, but it is the assumption that lies behind the allocation of classrooms for Fall 2021. If your lecture is remote, no rooms have been reserved for you for midterms or for finals. This is true whether all, some, or none of the associated discussion/lab sections are in-person. 

If your lecture is remote and you want to hold in-person midterm exams, you have two options. One is to hold the exam during the discussion/lab sections since those students already have a room to meet in. With multiple sections, though, this might require multiple exams to ensure academic integrity. The other option is to hold the exam at a common time, perhaps in the evening. In this case, you need to work with your department scheduler asap to try to reserve rooms for the exams. Space availability may be the binding constraint. Flexibility will be important, both for the usual student athlete/musician/etc. and DSP accommodations as well as for students who were unable to travel to Berkeley due to international travel and visa restrictions.