I think there are at least three cases where science has gone wrong so far.
1) The first case is that physicists have found that the total energy of our present universe is zero. On the basis of this fact they have concluded that the entire universe has originated from nothing. But this is a wrong conclusion, because I have already shown here1 that the total energy of the universe would also be zero even if it has originated from something and not from nothing. So zero total energy cannot be the only criterion on the basis of which it can be concluded that the universe has originated from nothing.
2) The second case is that if we take it for granted that the universe has originated from nothing, then not only its total matter and energy, but its total space-time as well have also originated from nothing. So not only its total matter and energy, but its total space-time also should always remain zero, because space, time, matter and energy-all the four of them have originated from nothing. Something can come out of nothing provided that the totality of that something always remains zero. So total space, total time, total matter and total energy of our present universe must always remain zero if it is claimed that the universe has originated from nothing. Although scientists have shown that the total matter and the total energy of the universe is zero, but they have not yet shown as to how the total space and the total time of the present universe also remain zero. This is one major drawback in their theory that the universe has originated from nothing. And if this theory cannot explain as to how the total space-time of the universe also remains zero, then these scientists will not be able to convince us that universe’s origin from nothing is actually the case.
This point has also been discussed in detail here2 and here3.
3) The third case is that scientists have artificially created a vacuum and then they have observed that virtual particles are still coming out of that vacuum. From this observation they have jumped to the conclusion that something can actually come out of nothing. Then they have further concluded that the entire universe has also come out of nothing due to the quantum energy fluctuation in a void. But this conclusion may not be a sound one, because first of all it will have to be ascertained as to whether the void created by them is a real void or not. Scientists have created a void within the universe and not outside of it. If there is a God, then that God is omnipresent, everywhere. So, if there is a God, then the void created within the universe will not be a real void at all, because in that case there will be the presence of God within the void itself. In case there is no God, then only it can be said with certainty that the void is a real void. So first of all it will have to be established that there is no God. Without establishing this point first if these scientists want to proceed further based on their assumption that the void is a real void, then all their conjectures, and all their conclusions based on those conjectures, might be proved wrong if ultimately it is found that there is a God. And to prove that there is no God it is necessary to show that there is no hand of God behind the creation event. That means scientists will have to give a natural explanation for the origin of the universe. This is because if there is a God, then definitely this universe will be his creation, and so if this natural explanation for universe’s origin can be given, then it will show once and for all that there is no God. And it will also show once and for all that the void is a real void.
But instead of doing this first thing first, scientists have already presupposed that there is no God when they have concluded that the void created by them is a real void. Then based on this presupposition that there is no God they have shown that no God is actually necessary for creating the universe, because it can naturally arise out of nothing due to the quantum energy fluctuation in a void. So this is nothing but a pure case of circular reasoning.
This point has also been discussed here4 and here5.