In the following thread:
https://bitcointalk.org/index.php?topic=289795.0you will see that we cuss and discuss where the ECC parameters come from, if they were possibly designed to be weak by the NSA, etc. I even contacted people on the committee that designed the ECC used by Bitcoin and asked them directly where the parameters came from.
I suggest a read of that entire thread. It is probably the most fascinating thread I have ever participated in.
Good thread indeed. I've always been more worried about potential weaknesses in ECC rather than somebody's ability to "decrypt" SHA256.