It is important to understand the underlying technology and politics of nuclear weapons deals. In order to build a nuclear weapon, the most important and difficult task is acquiring enough Uranium-235 or Plutonium-239 at weapons grade purity. This means that the key to building a weapon, and consequently controlling weapons development is controlling the refinement of U-235 (which is necessary for the creation on Plutonium-239).
The basic logic of the Iran deal are that 1) the deal will slow, not stop, Iranian U-235 production, and will force it to conduct that refinement under conditions observed by the international community, and 2) by bringing Iran back into the international community, there is now time to change the underlying political situation in the Middle East towards more stability.
Therefore the core criticisms of the Iran deal are these:
Verification of Iranian Enrichment is not sufficiently robust. The slowing of the refinement only works if Iran only refines Uranium at designated places, and those places are monitored. Iran could conceivably continue enrichment elsewhere, and the first assumption of the deal is invalid. Critics believe that the regime agreed to by the Iranians is insufficiently robust to ensure that they are only refining Uranium at the designated locations. As such the breakout time to a nuclear weapon, which is supposedly increased to a year because of this agreement, could actually continue to decrease and the international community would not know it until it is too late.
There is essentially no cost to violating the agreement. It was a long hard slog to put the current sanctions regime in place, and Russia and China no longer support the regime, but have continued to adhere to it. Signing this agreement drops multiple sanctions at once. The idea is that if Iran walks away from the deal, then the sanctions will "snap back" into place, but that is highly unlikely to happen. This means that Iran can basically do as Saddam Hussein did (for his own, confusing reasons as he did not have a nuclear program) and kick out the inspectors. Theoretically, the sanctions would snap back into place immediately, but that is unlikely to happen given the intransigence of Russia and China.
The agreement puts a seal of approval from the international community on a program that most countries in the region view as illegal. The Non-Proliferation Treaty states that only 5 countries have the right to maintain a nuclear arsenal the U.S., U.S.S.R. (now Russia), Great Britain, France and the People's Republic of China (PRC). All other countries have the right to have nuclear power, but nuclear power only requires ~5% refined U-235. Unfortunately, breeder reactors--popular in much of the world--also create Pu-239 which is usable in a nuclear weapon as well. The biggest problem is that Iran has previously insisted on refining nuclear material above 5% at about 20%, which is much closer to the nuclear weapons threshold, and consequently many observers believe that Iran is not building a power program, but a weapons program in spite of the fact that they are not yet making weapons. This means that by signing a treaty which accepts the current program, the international community is conceivably weakening future non-proliferation efforts.
The deal actually makes nuclear proliferation by other states more likely. One lesson that many states have taken away from nuclear politics is that it is very bad to be the last country without Nukes. Up until recently Israel was the only country with nuclear weapons, and they have only ever used them passively, such as when they coerced the U.S. to intervene diplomatically in 1973. Sunni and secular states in the region fear increasing Iranian power, and their willingness to intervene in other countries as they have in Lebanon, Syria, Iraq and Yemen, and do not want to be at a nuclear disadvantage. By removing international sanctions on Iran, it makes it appear that the international community at least tacitly accepts an Iranian nuclear program to these countries, and they no longer believe that they have the support of the U.S. and will develop nuclear weapons on their own, regardless of security guarantees made to them.
Even if the agreement decreases the risk of nuclear war, by removing the P5 from the war, it increases the risk of war in the Middle East. On the one hand, this may seem trivial since there are already ongoing wars in at least, Iraq, Syria and Yemen, but if local governments come to believe that the west is no longer securing their interests in Iran, they may take the issue into their own hands. There are already whisperings of cooperation between Israel, which has twice destroyed nuclear programs in Iraq and Syria, and Saudi Arabia. Saudi Arabia recently invaded Yemen to counter the growing power of the Iranian supported Houthis. Conceivably, further anti-Iranian cooperation could coalesce in the region into a Sunni-Shi'a regional war, all to prevent Iran from becoming too powerful in the region.
A similar agreement was signed before, with North Korea, and it failed miserably. Many observers have pointed out how the language of the current agreement with Iran and the previous agreement with North Korea are quite similar, and yet, North Korea has detonated at least two nuclear weapons since that agreement (i.e. the agreement failed). Defenders of the agreement will rightly point out that the U.S. and others basically reneged on their side of the agreement, but that is part of the problem. Many Republican congresspeople pointed out in a letter to the Iranian government that in order for the agreement to be law in the U.S. it has to pass the Senate, which it doesn't look like it will. If it is just done by the President, it is possible--but unlikely--the Supreme Court will stop it, or a future President can simply say that the previous President was wrong and renege. In essence, there are many, many reasons to question whether both sides will adhere to the agreement, and nuclear proliferation in the region is highly problematic.
I would add, that none of this is to say that these criticisms are correct, but they are prima facie consistent. The counter-argument is "The sanctions regime was about to collapse anyway, so anything we could get is better than nothing," which if you believe that the sanctions regime was unsustainable, then that is probably true. If you want a more in depth discussion of that side, you should ask another question.
