Whatever it is, Bitcoin network protocol?
As Bitcoin solved the "Byzantine Generals Problem", which means that any trusted third-party can change the public or open source algorithms.
Where is necessary trusted third-party?
Notaries, property registries, courts, voting, government, stock exchanges, corporations,..
All of this can be automated, open, transparent. No possibility of corruption or manipulation.
That the problem be solved without the imposition of central control point or hierarchy "trusted third-party" - all participants in the network must be equal.
That and it is the Bitcoin network protocol - open and transparent.
Is there Bitcoin protocol weaknesses?
Lack of anonymity?? If The private keys that are mathematically related to a distinctive Bitcoin addresses generated for the wallet - this is what is visible to all, it could be on gaps anonymity?
As Bitcoin transaction shall become effective only if it is in your blockchain copy inscribed and can see every Bitcoin user, therefore, not possible to carry out such transactions, which are not seen by the whole world. This means, that any person in the world can see as one of private key send BTC to other private key when and how much BTC sent - all this information is public.
But what this or other personality, no one knows
If you more interesting to learn;
More information about this lack of Bitcoin and its potential solutions, this is the lecture of Microsoft Research - Anonymous Distributed E-Cash from Bitcoin
51% of the possibility of attack. Since the agreement reached Bitcoin system democratic manner, which means that everything is going well, as decided by more than 50% of users (as measured by the Bitcoin network resources allocated to computer power). In order to meet the 51% of the attack, there should be more resources for computer power than the rest of the Bitcoin network. At present, the total amount of the Bitcoin network resources is a thousand times greater than the 500 most powerful supercomputers currently existing amount of resources.