Biggest problem with inductive reasoning is a huge leap of faith from specific to absolute.
It works in a way of "ok, so far everywhere we observed, A was true, so A is true everywhere, even where we didn't observe"
The leap of faith happens because despite the fact that induction holds true in areas which were observed, assuming it holds true in non-observed areas is simply impossible to conclude.
So using induction to prove an absolute claim is logically impossible no matter what.
The best example of failed induction is relativity of time. If you merely observed Earth, you could conclude a clock works just about same everywhere, with some small insignificant differences of time mismatch. If you observed parts of universe with different gravity and properties than Earth, you would come to an entirely opposite conclusion. Clock would show not just small mismatch, but an hour on Earth and an hour elsewhere would not be close to same. Hence, relativity of time which showed that time measuring instruments are actually not consistent in all areas in universe.
This same applies to gravity. While Earth's gravity remains true on Earth, it does not remain true anywhere else. Induction pretty much fails any time when observed area and non-observed area could mismatch.
We didn't observe even 1% of things in this universe alone, so basing absolute claims on 1% of area which we observed is a serious leap of faith.
Problem with induction is always going to be that as long as induction isn't based on observing everything there is, making a claim about everything there is will always be leap of faith.
Induction actually has two problems which science could never effectively solve:
1. Observing one area to make absolute claim about all areas
2. Observing one time to make absolute claim about all time
2 is actually pretty funny. You can never prove that what you observed to be true today will still be true tomorrow. Science proves things in present moment, but future moment represents a gap which induction cannot cover.