You seem to have heard that our improved understanding of genetics and other details of inheritance mean that Darwin's ideas have to be flawed because they did not yet contain this understanding; much like Newton's theories were supplanted by Einstein's and his in turn by parts of Quantum Theory.
But this is neither strictly not loosely true. Newton's theories are flawed, because they indeed overlooked an integral property of physical reality. Its formulas simply lead to values that are not correct in our universe. But, and here's the important difference to Darwin's theory of Natural Selection: Darwin never stated any formulas leading to precise predictions. He never explained the principle driving the changes needed by Natural Selection.
What he did was more subtle. He looked at the world and identified the obvious end-result: Species change, compete, cause their predecessors to perish (or change) and then finally perish themselves. Species are not static and unchanging. Instead, each organism is different from the one it sprung forth from. Given enough time, these subtle changes lead to large differences; so large that you'd not immediately see that they are related.
As such, Darwin's point was that Variations, Families, Races and Species are just "grouping terms". They fluidly flow into each other. Small individual changes lead to large cross-species differences.
This point is clearly not flawed. It is quite obviously true, if you look at the historical record and current progress. And that is his entire theory. He never stated what the principle behind the system was, as he could only suspect, not prove. This, he left for later generations. He freely admitted that, if no such system could be found, that his theory would have a huge problem. Thankfully, modern biological sciences has found this principle in all its differentiated glory from genetics, epigenetics, vertical and horizontal inheritance, retro-viral modification, genetic absorption, etc. pp. So instead of not accepting his model, they actually and knowingly vindicated it!
Of course, some of Darwin's larger speculations turned out to be wrong, but these were not the core of his theory of Natural Selection and clearly labeled by him as pretty much unsubstantiated speculation. Just go ahead and read "The Origin of Species" and you will see how careful Darwin was by stating exactly what could break his actual theories' back, which points he though could be proven beyond doubt and which are more doubtful.
So, tl;dr: His theory is actually vindicated by modern science; but it's not the theory of evolution but the theory of natural selection, as these two are quite distinct beasts.