That's a bit of a loaded question, because any two main problems are the interpretation and opinion of the reader. For me though, there's a whole host of problems going on in "The Giver."
1. The Sameness. I suppose that all of the problems are a result of The Sameness, so I'll pick some specifics. Everybody is supposed to look and act the same. Eye color, language, hair cuts, etc. It's all supposed to be the same. That means there is no individuality. For an American, that's a major problem. The Bill of Rights is all about the individual's rights and freedoms of expression. Biologically, genetic diversity is the reason that species are able to adapt to changing environments. Everybody being the same means that anybody different is persecuted. And in "The Giver" this means killed (but nobody seems to know that).
2. Emotional neutrality. Nobody seems to be genuinely happy or sad or angry in "The Giver." No sadness, hatred, or anger sounds nice, but isn't. I had somebody ask me one time: "If you never knew sadness, how would you know happiness?" For any two opposite emotions, the reason that you experience them so strongly is because you have the ability to compare it to the complete opposite. If I never knew sadness, then my "joy" would simply be normal. It wouldn't be joy, it would be neutrality. Basically the society in "The Giver" isn't only emotionless, it is passionless.
3. All of the rules. There are rules for everything in "The Giver." Rules are not bad by themselves, but in "The Giver's" situation, they are just there for further control by the government. There is no trust in the human population to govern any of their behaviors. That's sad. Also, some of the rules are just plain silly. Like not being able to ride a bike until a certain age. Which brings up another problem of having so many rules. If you make a rule, you have to enforce it. That requires manpower hours and money. Just to make sure an 8 year old doesn't ride a bike? No good.