Is it acceptable, if too many students in the class would fail otherwise, to award additional points across the board (in the one class, in one semester)?
Would it require approval of the Division Dean? How could this be justified?
I would say, in nearly all cases*, it's unethical. Specifically, if a student's submitted work does not fulfill the requirements for a passing grade, then they do not deserve a passing grade. Arbitrarily adding points that do not reflect the quality of submitted work makes the grade partially or completely useless as an indicator of performance in the class, and if it's not good for that, what's the point?
However, unethical does not necessarily mean unacceptable. Don't get me wrong, I think it should, but I'm not going to impose my moral standards on your grading scheme. Ultimately nobody on this site can tell you whether it's acceptable to do this. Your superiors at your educational institution might be able to, since they'll at least know whether it would violate any of the institution's rules.
In any case, as a few people have mentioned in the comments, arbitrarily adding points to keep students from failing is a band-aid effect. The fact that too many students are failing indicates that there is some deeper problem. Perhaps your teaching is inadequate. Perhaps your grading standards are too harsh. Perhaps the students are not properly prepared for the class. Perhaps your idea of what constitutes "too many students failing" should be revised. And so on.
*Speaking of harsh grading standards, this is (the?) one case in which I think it is ethical to add points: to compensate for an overly difficult exam or assignment. This is a little tricky to get right, though. You have to have a preexisting standard to measure whether the exam is at an appropriate difficulty level. For example, in classes I've TA'd for, there has been a longstanding policy that any time the average grade on a test (across ~1000 students) is less than 70%, it will be taken as an indicator that the exam was too hard, and therefore enough points will be added to everyone's exam grade to bump the average up to 70%. Given the large class size, I think this is reasonable.
For smaller classes, you have to consider the possibility that you just have an underachieving group of students one particular year. In another (small) class that I took, each year the instructor would compute the distribution of all grades in the class over the previous ten years, compare that to a desired target distribution, and make the course material for the next year harder or easier as needed. From what he told me, it gave pretty consistent results. I think this is a good way to do it.
The key is that you have to have a preexisting criterion for when points will be added. If you look at the grades after the fact and decide, hey, too many students are failing, let me add some points so we all look better - then you're doing it wrong (IMO).