Ask HN: Can we consider the web safe now?

I am not a security expert but the heartbleed bug, that leaves almost no traces, has affected a big part of the internet (some say over 50%, others over 70%), and I think that it is pretty much impossible for the most of it to be quickly updated. So will we live with the consequences of this bug for a few years? And how can we be sure that bugs like that aren't included in other commonly used libraries? Please let me know I am mistaken.