For each course (Moodle 1.9) I run 3 times a year, I receive ca 950 assignments and quizzes to mark manually. These arrive uncoordinated from students around the world.
A plea for the next version of Moodle. Provide a method to sort and access unmarked work by a number of criteria, e.g. date of submission, student, quiz/question number, assignment.
The Moodle Forums may not be the appropriate place to request something like this. You can create a Moodle Tracker for a new feature request; that way the core developers actually see the issue.
I'm not sure what version of 1.9 you are running but I am running 1.9.11 and it does have column headers that allow you to sort in assignments and quizzes. All the column headers in the picture below are clickable and sort just like an Excel file does. If you are trying to locate ungraded submissions, sort by grade.
Happy 
oodling!
That's per activity, but I think there is no way to access all the activities of a selected student from one page (the student activity report lists the activities but the links lead to the submission page of the activities).
Yes - but
Taking just the assignments.
There are 24 assignments from 35 students who can submit their work at any time during the course.
The need is to identify all the ungraded assignments then tackle them in blocks by student so as to get an overview of the individual's progress. But one can only search through the assignments one by one, through all the clutter of the marked and unsubmitted ones, which are not relevant. Or is there a better way?
Finding unmarked quiz questions is even more painful.
And then, It is quicker to mark using a red pen on paper than typing comments on assignments (Word or pdfs) or in quiz comments boxes.
All of which makes the marking load about 30-50% greater than paper.
So what I am asking for is a far more efficient method of managing the assessment process.
Not to be argumentive but your statement of "a far more efficient method of managing the assessment process" I think is a little subjective. I administer a Moodle instance that has over 35k active users and 3k courses each semester. Our faculty is about 2k of those users. In my time as an administrator, I have got about half a dozen requests for something like you are asking; to be able to grade all of a student's assignments in one spot vs. all submissions for a single assignment in one spot. So your argument has been thought of by others and is valid. However, I think the vast majority of users prefer the method that is currently in place.
So to your goal, I don't think is possible at this time. You can sort by grade to get all the ungraded assignments together but you won't be able to get all ungraded assignments of a single student in one spot. As mentioned you can put in a Moodle Tracker feature request but that doesn't mean it will be done.
Finding unmarked quiz questions though is really easy though. When looking at quiz results, each question has its own column so you could sort by the column to get all the ungraded ones together; again that won't be by student but all the submissions together. If they are manually graded questions (i.e. essays), in the quiz submissions tab there is a manual grading method that makes it easy to find the ungraded questions.
Adding comments to assignments is probably best/easiest if the assignment was an Advanced Uploading of files assignment type. This assignment allows for response files. So if a student uploads an MS Word document, the teacher can download to their computer, use MS Word Track Changes for edits/comments, upload the response file and then the student can download the response file to see comments.
Happy oodling!