The simple answer is no. Some people have tried to point out that there are contradictions, but this is just their misunderstanding, lack of understanding, or lack of care to try to understand the Quran in light of itself.
Muslim commentators say that the Quran is explained by itself. Part of the Quran will interpret or explain another part. Something may be said in brief in one place but detailed further in another place. Or one aspect of a story may be a shared in one place and another aspect is shared in a different place. But they're not contradictory or even contrary; they're just different aspects of the same issue.
For example, some have pointed out that while the Quran clearly says in many places that the heavens and the earth were created in six days, the Quran in 42:9-11 gives the number of days for various aspects of the creation which, when added up, is 8 days in total. Indeed, there is a mention of two and four and two again.
If it was a sequential narrative, then it would make sense to add up the number of days. But the Quranic language is very subtle. There is a connector which is used in Arabic, fa, which suggests a sequence, and there's another connector, thumma, which could indicate a sequence, but it could also just refer back to something that was already mentioned, or it might offer some additional information. Dr. Maurice Bucaille in his book, "The Bible, The Quran and Science”, pointed out that the first mention of two days for the creation of the earth and then the four days for putting the sustenance in the earth give us the six, which matches what it mentioned everywhere else in the Quran, i.e. that God created the heavens and the earth in six days. The final mention of two days is the mention of the same original two days which were already previously mentioned in reference to the earth, but now it's mentioned in reference to the heavens. God turned to the heavens when it was smoke and said to it, "Come either willingly or unwillingly." So this is a mention of the same first two days. We still have six days, two days plus four days, and then it refers like a flashback to the original two days. It's not two plus four plus another two. It is still six days.
Some pronouncements in the Quran have changed (e.g.) alcohol rulings. Muslim scholars have explained that within the 23-year span of the prophetic period (beginning when the Prophet, peace be upon him received revelation and ending when he passed away at the age of 63), there were many different and changing circumstances.
The Muslim community came from a period that is referred to in our history as the period of ignorance, and suddenly they were being given new regulations about Islam. They needed time to adjust. In the early stage, they might have been given a sort of a lax ruling, and then later on a stricter ruling. Both are mentioned in the Quran, but they must be interpreted in light of each other. These are not contradictory rulings. It's more so like something is not said.
For example, they are asking about alcohol and they were being told, "Alcohol has some benefits, but also a lot of harm, so think about it." This suggests that alcohol is not welcome in the Quran, but it doesn't specifically say you have to give it up. Only later does the Quran say, this is from the work of the devil. So leave it altogether. This later verse is not contrary to what was said before, because what was said before was simply an answer to the question, is alcohol good or bad? And the answer is, it has some good things, but much more bad things about it, so use your judgment. And then later on it's saying that you can't have it at all.
If you are concerned about what seem to be contradictions in the Quran, you can clear up your concerns by looking at commentaries on the Quran. A commentary will reference a verse and explain that it has to be understood in light of another verse.
A commentary will then bring it all together, explaining that at first Muslims were being told that alcohol has more bad than good. Second, they were being told, if you drink, do not come to the prayer because you must be sober first. And lastly, they were being told, now you can no longer have it.
Laws can change as time and circumstance changes. We know this also from the Bible. An old law might have been given and then Christians believe that a new law was instituted through the life and teachings of Jesus, on whom be peace. Muslims believe that the Quran brought a new law altogether, but even that new law was given gradually in stages. There is a prescription for every time and circumstance.
