There isn't anything magical about the number 51, the original Bitcoin paper gives a program that can be used to compute the success probability for an attacker with a given share of the computing power to reverse transactions to a given depth... At >=50% the probability becomes one but at that point only if the attack is of infinite duration. But, for example an attacker with 40% hashpower can reverse six blocks with a 50% success rate.
Any kind of consensus system is going to be vulnerable to a majority attack of some kind— otherwise you'd have "minority imposes a wrong outcome" attacks.
At least in Bitcoin the "consensus" only controls transaction ordering: a majority attacker can't inflate the supply or spend other people's coins... they can only DOS and remove transactions from the fixed consensus (and thus replace their own). Which is powerful but still limited.
In the case of Bitcoin there's the 51% attack, which is pretty serious flaw even if to carry it out is unfeasable.
We don't know if NSA or GCHQ have broken bitcoin (although they've certainly investigated it); and we haven't seen much crypt-analysis on it; but we have seen very many people trying (sometimes successfully) to attack Bitcoin and the wallets and the exchanges.