The first thing I want to say is that you should be careful with the information you provide on the internet. In ten minutes of routine searching I was able to determine the identity of your instructor and other information about him: e.g. he is 84 years old, that his highest degree is a master's degree, and that he is (as mentioned) not tenure-track at your institution. Thus you have publicly enough claimed that someone is senile. That opinion is yours to express...but it is not very nice. If you have not already had at least one conversation about the instructor himself about what you find unsatisfactory about his teaching, then complaining about him to everyone is not an honorable thing to do. I think it would be better to remove identifying details from your profile.
Now moving on to your question: I think you have at least two issues here. The first is that you claim that rampant cheating will put you at a disadvantage in your classes with this instructor. The second is that you think the instructor is unfit to teach at your institution. These are pretty different: one of them is localized to a particular situation and is primarily about you. The other is a general problem and is primarily the concern of the institution. I would recommend decoupling these concerns at least in your own mind and thinking about how to pursue them separately.
As for the first concern: is the cheating you're describing taking place in a class you are now taking? Your question suggests that but doesn't quite say it, and in my internet research I couldn't find any courses that the instructor in question is teaching this semester. If yes, this is a pressing issue, and of course you should bring it up first with the instructor himself. Does he know that students are cheating by looking at their phones in class? What is his response to that? If he hasn't been informed of the cheating, it is not very reasonable of you to blame him for it. If his response is "I don't hold truck with those devilish pocket phones" then that's inadequate and merits escalation. It sounds however that you're trying to bring forth action on a more generalized "everyone knows this is happening" cheating situation that may not even be taking place this semester. That's going to be hard to do. You lament that many students complain about this but are unwilling to do anything formal about it. You're right to lament, because that probably will kill the matter right there. I am a university professor and I've had the experience of students who complained to me about cheating but were unwilling to take it any further. That was very unpleasant for me, because there was nothing I could do about it....other than make sure that the circumstances that allowed the cheating did not present themselves in the future.
In terms of your second concern: whether this man is fit to be an instructor at your regional campus of a state institution is primarily the concern of that institution. I am not trying to say that this is none of your business. What I'm saying is that it's more their problem than yours, and you should take the attitude that you are helping them out by informing them about it. Do you see what I'm saying? If you come to an administrator saying that a certain instructor is not fit to teach...and you are not asking for any personal reparations for that in your own coursework, then it puts a different spin on things that may make the administrator take it more seriously. (That's why I would consider separating out discussion of this with the cheating issue: if you discuss them at the same time, then it can look like you have a conflict of interest, because something good could happen to your course grade if the instructor's incompetence is recognized.)
In terms of informing administrators that the instructor is unfit to teach: you have to realize that this is a long game. It is extremely unlikely that someone is going to get pulled from teaching in the middle of a semester for reasons of "senility". Firing a faculty member -- even a temporary or untenured one, and especially someone who has been working there for many years -- is not something to be done lightly. You can't really know that the administration is not looking into this or will not look into this in the future. Maybe they are. However, in the absence of any positive evidence, yes, maybe they're not. In that regard Dan Romik's advice is on point: bring this up repeatedly. If other students feel the same way, get them involved. (If really no one other than you wants to get involved...what's up with that? It's worth thinking about.)
Another thing that students don't necessarily appreciate is that universities have limited resources, and the in current economic climate many academic programs are being held together with string and chewing gum. Every once in a while I get an evaluation from a calculus student saying something like "Dr. Clark knows his math, but I'm not sure if he's ready to teach UGA students." Which makes me smile a little bit: I was a tenure-track (now tenured) faculty member. Do the students think that teaching freshman calculus is a privilege only earned by the very best, and that some time in the penalty box would make me rethink the error of my ways? That's just not the way things work. At my university faculty members get tenured for excellent research and unproblematic teaching. Freshman calculus students are going to be stuck with my teaching -- which, according to student feedback, is below the departmental average -- for the foreseeable future.
At your institution I noticed that there are a lot of non-tenure track faculty, often without PhDs, teaching courses for majors. Your administration would certainly prefer if such courses were taught by people with PhDs: it would add considerably to its academic prestige. The fact that they have courses taught by non-PhD faculty probably means that they have limited resources and/or haven't had the chance to do enough hiring to correct the problem. To put it more starkly: if your octogenarian instructor gets released, who will replace him? If they don't have such a person, then they are probably working towards getting one and thinking that in the meantime he is a lot better than nothing.
I will end by saying: you are right to be concerned about this, and if what you say is true than in my opinion you are helping out your university by doing so. Good on you, and I hope you follow through with it. Definitely do not do anything like publicly shaming your university by uploading incriminating videos: that is not a step towards a solution of the problem.
Added: Based on information provided by the OP, I have changed my mind about who the faculty member is. I now believe he is 79 years old. Anyway, the point is that when you reveal your institution and department any complaint about faculty members is certainly not anonymous. Any slightly interested party can make a guess. Maybe they will guess wrong...which is not so great either.