The mathematics are sound enough, but that doesn't make BitCoin sound.
After the MtGox situation, I tried to understand what exactly the transaction malleability problem they're blaming is. The best (?) starting point I've found is https://en.bitcoin.it/wiki/Tra..., but while that gives you a high level overview, it also raises more questions. Why are there three distinct issues with BitCoin that share the same name? Why did the BitCoin designers ever think it's a good idea to take a signature over part of a message as verifying the entire message?
Mostly, though, I asked myself what it was they were signing and for what purpose, before going on to the previously stated questions. Several hours later, and I concluded that BitCoin is the single worst documented software system I've seen in a 15 year software engineering career.
Yes, I managed to get the information I wanted. No, it wasn't straightforward. Documentation is distributed amongst this wiki, forum posts (which are then badly copy & pasted into the wiki) and source code. Oh, and external sites like reddit or stackexchange. The wiki is very badly cross-linked, and the terrible naming choices (see above) mean it's not easy to search. Some vital information is effectively hidden from sight in image files, which wikis currently don't tend to index at all. And that's just about the stuff I was interested in at the time.
You should never trust a crypto system whose authors can't explain it cohesively and concisely.
If nothing else, it makes a security audit a nightmare.
That said, of course the BitCoin devs aren't stupid, and they plugged the holes documented in the transaction malleability page as best they could. The wiki still states they exist, incidentally, and since it's the de-facto documentation on BitCoin, it's IMHO fair enough to conclude that the BitCoin specifications are still broken even if the reference implementation is fixed.
None of which should mean that BitCoin itself did worse that MtGox - the latter certainly screwed up royally, and their screwup doesn't mean BitCoin is doomed.
But nothing I've seen of BitCoin so far goes to convince me it's trustworthy.