You need to decipher his hand-written homework, notes, and exams. Trust me, it's not as easy as it sounds.

I don't know why everyone seems to think he's not a good professor. If you don't understand anything go to his office hours, he won't ignore you, he will guide you through the concept. He is, however, reluctant to simply state the answer so much as it is his method to make you think for yourself.
All in all, I'd recommend him. Personally I look for classes he's teaching when I pick my courses.

Terrible terrible unclear professor. Garbage handwriting terribly written textbook non-standard terminology on exams teaches out of lecture notes which are undecipherable due to said handwriting refuses to use standard textbook assigns problems of weird difficulties (not necessarily difficult sometimes they're just weird) RUN AWAY NEVER TAKE HIM EVER HE'S REALLY REALLY REALLY BAD and I've never left a bad review for a professor before (not even Gieseker)

I have mixed opinions on Greene. For example, he does give a lot of practice problems and those help (and sometimes are the exam questions). However, he is very unclear sometimes. We also covered a lot more than was expected which I wouldn't mind if it were a regular 10 week course but as a 6 week summer course, it felt way too fast. He also didn't give any personalised feedback (just overall comments) about the final so I have no idea why I received the score I got. The grading seemed very polarizing. I think the TA graded too easily (which Im not complaining) so when the prof graded the final, my grade hit me like a truck. Also, had I not taken 131B before, I wouldn't know how to do some of the problems (though maybe there were gaps in my knowledge and could only figure out how to prove it with 131B techniques). However, 132 as a class is very interested and glad I took it. I just wished there was a bit more transparency

I don't know why Greene is rated so low. Sure, he has bad handwriting that can confound students when they try to read homework, lecture notes, exams, etc. Sure, he sometimes writes on the board in a disorganized manner, moving from one place to another, which is only made worse by the handwriting. Sure, he sometimes goes off tangent to tell stories about dogs and other aspects of his life. And sure, he has a heavy dog odor that is often unpleasant for people like me. But I did not think he was that bad. There were not that many topics covered in Math 132, so for the most part the pacing felt a bit slow compared to other classes.
As for homework, Greene does not give very much, though be warned, you should complete them with the utmost detail and rigor, in case your TA is very nitpicky like mine was. Homework does count, as it is 20% of the final grade, and none of them can be dropped. Most of the homework is straightforward, as Greene usually discusses the ideas during lecture. If that isn't enough, both Greene's and probably the TA's office hours can help, which by the way, are evenly distributed throughout the week to ensure anyone can come.
As for exams, although they might be time-consuming and perhaps difficult, they are nonetheless fair. This is because Greene basically gives the exam away long before it is handed out on paper. He provides online lecture notes, and he also provides sample exam problems. The material on the exam is 100% guaranteed to come straight from the sample problems, so as long as one understands how to do all of them, they can essentially ace the test easily. He also tells the class way ahead of time what part of the final will be. In fact, there were many instances during lecture when he solved potential exam problems including the sample problems. Thus, Greene's exams are very fair and straightforward.
As for Greene himself, he may be old, but he is a very nice man. One of the things I found interesting was that he would always lecture with a smile on his face. His office hours are quite helpful, as he is willing to guide students step-by-step in their problems and explain the concepts carefully.
Overall, while I did not find this class to be particularly great because lectures were often unclear, I don't think the ratings should be that low. Greene just wants his students to succeed.