If so, why did appeals not confirm/pick up on these flaws, if they were legally compelling?

Well, U.S. law has some interestingquirks- look up Supreme Court case Herrera v. Collins, 506 U.S. 390 (1993)

Then there's Justice Clarence Thomas & Justice Antonin Scalia who criticized their colleagues for thinking that mere innocence is grounds to overturn a conviction:

    ""This Court has never held that the Constitution forbids the execution of a convicted defendant who has had a full and fair trial but is later able to convince a habeas court that he is "actually" innocent. Quite to the contrary, we have repeatedly left that question unresolved, while expressing considerable doubt that any claim based on alleged "actual innocence" is constitutionally cognizable.""

I could go on......