Darwinism claims that an organism will pass down its genetic traits by reproducing more. The more successful the trait, the more chances to reproduce and the more likely it will pass on. As for the flaws of Darwinism itself, it cannot explain a lot of things:
-Sexuality: Sexuality is wholly unproductive. To require another organism to procreate is a great hindrance. It is much more successful to reproduce asexually. Yet Most multicellular organism are sexual organisms. This does not hold for Darwin's theory.
-Homosexuality: Homosexuality is even more unproductive than heterosexuality. You cannot reproduce in engaging in homosexual sex. Yet, there are entire species that build their society around homosexual behavior. It would be much more productive to completely eliminate this gene out of the genepool. Yet it isn't. (this point is under the pretense that homosexuality is a born trait, not a learned trait.)
-Protein Building: As science develops, evolution has more holes in it. We are finding that genes do not control everything; protein structures do. And these cannot be passed down via genes. Therefore, and organism that has a "disorder" that gives the organism a protein structure that enhances its reproductive capability, then its genes get passed down even though its genes did not offer anything beneficial.
-Sexual tenderness: Many species have the male getting consent from the female before intercourse. This methodology isn't logical. Aggressive rape would increase the reproductive chances of the organism. And because aggressiveness is related to hormones, which are related to genes, aggressiveness can be passed down. (There have also been studies down that show that domesticity, AKA non-aggressiveness, is genetic as well.) But most species are not. Males do not just go around raping every single female he sees.
-intermediate species: Because Darwinism claims that evolution is a continuous process, the biological composition of the earth, both present and past, should be continuous as well. Yet we can clearly classify species and find clear distinctions. Even with more "intermediate species" being unearthed, the Tree of Life is very must patchy. This is a great obstacle that needs to be overcome.
-Humans: Humans clearly have highly superior traits than other animals. Yet there are no other animals like us. There are many felines; there are many rodents; there are many fish; there are many reptiles; there are only 1 living species in the homo genus. We are clearly different from all other animals. We change the environment around us; the environment does not change us. We have a mental capacity unseen. Why are we the only ones? Darwinism would give rise that the probability of multiple human-like species is high considering the highly successful nature of our traits. But this isn't the case.
I could go on about the many things Darwinism cannot explain, other than "well, it just chanced that way" which is no greater than creationists. Darwinism has a lot to go before it can be considered a true scientific theory.