The preamble declares this to be a "declaration the natural, unalienable, and sacred rights of man." Article 1 contradicts this by allowing government to make "social distinctions" founded upon "the general good." This means that when Hitler wants to genocide Jews, and is confronted as violating rights specified in this document, he needs to claim that the Jews are a lesser race and that exterminating them cleanses the gene pool and helps the general good. Having made that claim, Hitler is no longer in violation.
The "general good" doesn't exist. There is only the good of particular individuals, and by sanctioning "social distinction" based on "general good," this document allows governments to violate certain individuals' rights in order to reward certain other individuals. This creates pressure groups which compete for being perceived as representatives of the general populace in order to attain government handouts.
Article 2: "Security" as a right. The rights to life, liberty, and property, being proper rights, place no obligations on other people to provide anything for us. Unless someone takes action, we posses our life, we are free, and we maintain ownership of our property. These proper rights merely assert that no one may kill us, imprison us, or steal from us. They are "negative" in the sense that they place only a negative obligation on other individuals--the obligation to abstain from taking specific actions which cause particular harm to us. But what does right to security mean? If I take a job in which my continued employment depends on my achievement, I am lacking "security" because someone better qualified than me might always come along and force me to look for a job which I am more qualified to do. I am, according to this document, justified in suing the employer who discriminates based on ability because said discrimination violates my right to security.
Article 3: It is unclear which body aside from the individual is forbidden to exercise authority by article 3. In fact, the sole purpose of article 3 seems to be to assert government authority over the individual.
Article 4, by asserting that "liberty consists in the freedom to do everything which injures no one else," destroys the notion of the right to liberty. By acting to win the love of a woman, I am injuring other men who might have had her love had I not acted, and thus my action is not protected by this document. Properly, libery consists in the freedom to do everything which does not violate someone's proper rights (i.e., life, liberty, & property).
Article 14 seems to make taxation voluntary, but by saying that the citizens have a "right to decide, either personally or by their representatives," it ensures that no particular citizen will have the right to refuse taxation, as such refusal can properly be established by refusing to vote for politicians who tax.
There are other problems with the Declaration, but they are left as an exercise to the reader.