How should you approach your adviser and tell him that he has a communication problem

I would advise you to approach him on a different base than he has a communication problem, namely on the base that you have a problem with his way of communication. Note the slight shift.

Phrasing it that way eliminates the problem that you may accuse him of something or even offend him. For example, you would not say "your handwriting is poor" but "I have a hard time to read your handwriting and it costs me a lot of time to read it". Also, you would not say "your slides are unclear" but "I do not get the main idea from the slides and would find it helpful if [...]". Finally, instead of "your notation is unclear" you would say that "I consistently get confused since the book X uses the notation Y while you use Z".

I can understand your frustration, I have an advisor right now that has some of the qualities you have mentioned (points 1 and 2)! Here is my take on your situation.

Facts;

1. He is an older and busy professor => I'm sure he has heard many complaints about these points before. I'm even sure his colleagues and dept. chair know that too! Guess what, he is still the same, he will be the same. My advise to you is learn how to adapt. My adivor's had writing is really bad and we (his PhD students) keep old drafts of his writing with marks up of words that we could not get the first time just in case we need to decode his writing from a current draft! We all faced this issue once we joined his team. We would go to his office just to ask on how to read certain mark ups he wrote on our drafts and papers! To be honest, we tried to introduce him to the very simple and friendly Word "track change" but he politely said that this is not the way to teach and correct drafts. He only requests hard copies of manuscripts to go over and only asks for the soft copy once the paper is ready to be submitted. Also, he gets annoyed if he sees any of us reading/reviewing a paper or a draft using the computer, he would simply shake his head and say, "Kids these days!" (smiling and in a funny way). Honestly, I used to hate that but now, this is what I do. I still use pencil and a hard copy of the paper I'm reviewing or writing. To be honest, my advisor is right in a way. I agree that it is not the best/optimum/environmentally friendly way to do research (by printing pages and pages of drafts), but papers really sound and look different when you hold them in your hands. As I said earlier, to each his own, but since you are his student, you do not have to agree with him/her all the time! But, to keep your work going and avoid delays and arguments, you might want to do things his/her way! I believe that each student should has his own scientific charisma, but so far you are still a student so you might change your views if you try new (or in this case old school) stuff!
2. His note are all over the place and 1/2 the people stop following him and it is noticeable. If it noticeable to you, it must be noticeable to him/her too (during all his/her years of research and teaching)! Keep in mind that slides or presentations need to be somehow clear and easy to follow. But, they also do not need to be colorful and include cinematic effects! Perhaps to your advisor, having clean cut presentations is not that important. S/He cares about the science only. I would suggest that you offer to fix 1-2 of his presentations. Change them into something completely different. Arrange them in a way you would do your own presentations. Then, show them to him, perhaps he will like them and change the other slides (or most likely, will ask you to do change them).
3. Unclear notation => read point 1 above again.

Finally, being a graduate student is tough. The truth is, if you look closely, many PhD students turns to be like their advisers (in a way or two). How many of us have said "he (your advisor) does not know hat is he talking about?!" or "That does not make sense, he (your advisor) must have not read the previous page". But that is ok, I'm sure our students will say the same one day!

Having daily contact with someone can and will change the way you do or see stuff. Simply put, try not to over think such things that are annoying you and focus on the positive aspects. Your advisor is a nice and knowledgeable guy! Trust me, this is a hard combination to have in an advisor!