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I don't think these are really "exceptions" to any rule, nor have I seen any instances in which the gradebook is calculating grades incorrectly. I do see cases where the gradebook is not calculating grades as the instructors intends, but that's due to the gradebook not being set up correctly for the grading scheme. Sorry, but I think your belief may be a little flawed. I'd like to go through an explanation of how grades are really calculated in the gradebook. If you get to the end and still think you've found a case in which the gradebook is not calculating overall grades correctly, please check for extra credit or formulas being applied to categories or assignments. I'm not going to get into formulas or extra credit here but they can be used by an instructor to radically change how the gradebook calculates overall, category, and assignment percentages/grades. If that still doesn't explain it, email me the course ID (from Manage > General Settings) and an explanation of how grades should be calculated. If there's a bug we definitely want to know.

Points mode

If the gradebook is in points mode categories don't matter in calculating the final grade at all grade. The final grade is the total number of points earned divided by the total number of points available. The categories are used only for organization and for allowing the instructor to see average scores based on category.

Percentage mode

Percentage mode works differently than points mode and has many nuances.

The overall grade is calculated by using a user's weighted category averages. When calculating the overall grade, the point value of assignments doesn't really matter. It may seem like they do, but they really don't. It's the category percentage overall that matters—note that this can be a different value than the category's weight. The percentage overall is the weight for that category divided by the total weights of all categories (I'll get to this later). It's the percentage that a category "counts toward" a final grade.

This could be why you perceive the calculation as being incorrect in "exception 2."

Let's say you have a category that has a percentage overall of 80% and one that has a percentage overall of 20%. The instructor might intend for quizzes to count as 80% of the final grade and homework 20%, for example. If a student has an overall average of 90% on quizzes (category 1) and 80% in homework (category 2) then their overall grade would be calculated like this:

overall grade = (category 1 average * category 1 percentage overall) + (category 2 average * category 2 percentage overall)
overall grade = (0.90 * 0.80) + (0.80 * 0.20)
overall grade = 0.72 + 0.16
overall grade = 0.88
overall grade = 88%

The calculation of category averages is simple: the total points earned on assignment divided by the total number of points possible.

That said, the next thing to look at is how weights are used and percentage overall is determined.

This can be done one of two ways: 1) the instructor can set an explicit weight for the category; or 2) the autocalculate feature can be used.

If an explicit weight—the value in Gradebook > Categories > Category > Weight—the weight and percentage overall won't ever change even if assignments are added, removed, or have their points possible change.

If the autocalculate feature is used, the category weights will change depending on the points possible in all assignments in the category.

Continuing the previous example, let's say that the instructor originally intended to give three quizzes worth 50, 20, and 10 points. Homework (the other category) has a number of assignments worth 20 points total. At some point in the semester, the instructor decides to add a fourth quiz worth 10 points.

If the instructor set the weight for category 1 to 80 and category 2 to 20, the addition of the new quiz won't change the weights or percentage overall for either category. Quizzes still have a weight of 80 and overall percentage of 80%, and homework a weight of 20 and overall percentage of 20%.

But, if the instructor had instead checked the "autocalculate" box instead of specifying a weight the situation would be very different. Remember, autocalculate means that the category weight equals the total points possible in a category. The homework category's weight is 20. The quiz category's weight is 50 + 20 + 10 = 80. The sum of weights in the course is 100. The quiz category has a weight of 80 and therefore "counts toward" 80% of the final grade (80/100 = 80%). The homework category has a weight of 20 and is therefore 20% of the final grade (20/100 = 20%). When the instructor adds the fourth quiz the weight of the quiz category changes to 90 (50 + 20 + 10 + 10). The homework category does not change and still has a weight of 20. The sum of the weights of the two categories is now 110 instead of 100 and the two categories are now worth a different proportion of the final grade: the quiz category is now worth 82% of the final grade (90/110) and the homework category 18% (20/110).

Another way that weights can trip you up is if you think of weights and percentage overall as being the same thing. The only time when that is true is when the weights add up to 100. In a lot of (probably most) cases they do add up to 100 because the instructor sets them up that way. If you have a syllabus that specifies that quizzes are worth 75% of your final grade and attendance 25%, the logical thing to do is to create a category named "quizzes" with a weight of 75 and one named "attendance" with a weight of 25. However, you could just as well set the weight of "quizzes" to 3 and "attendance" to 1. Or 86.25 and 28.75. In all cases, the quiz category would be worth 75% of the overall grade and attendance 25% and the overall grades would be exactly the same.

Does this help?