The failure of science isn't in its methodology... but the public's view of science. The question of why the universe exists, or the meaning of life... you can't answer using science. But the public doesn't see it. They still try to throw science at every darn problem they face. And that's where the failure lies.
Just to be clear, this works both ways. There is a major failure when religion tries to be science (I think of ID notably here, but history is full of issues like this) too. And I think it works more in that direction than the opposite, although it probably is reaching a crossover point now.
Science, when compared to faith, does things very well in the physical world. It's a system of organizing information. In my view, it sums up type I/II errors on its own... except that the system is meant to constantly increase it's knowledge (sample) in order to drive down error. Faith doesn't operate like this, and so it is a poor system for gaining knowledge. That's inherent in any system that presumes knowledge.
But science, when compared to religion, or a specific form of religion, shows more commonality - and the commonality is people. People are people and have the same wiring... and so the essence of how we express it is very similar. The knowledge is agnostic to its source. We cannot possibly understand and discover everything, and so we filter and record opinions more than form them through any method. Science and religion, for the most part are very similar. Be it a monestary or a university. Granted, they have differences due to the differences in knowledge taught - at least in the modern world - but the concept of learning everything rather than just accepting some at face value... it happens both ways. And just like 'science', in common use, isn't uniform across the population, neither is the belief in religion. Some are really bad at 'science' and take it at face value, and some are very skeptical of religion. This underlies the basic issue: people and how we deal with information and knowledge.
The distinction is important because certain statements are not true under both comparisons. For example, can science answer questions about 'why'? It can, for sure, as a system. If you inherently assume that the only things that exist are natural (ie: if it exists, it's because it has an influence, if it has an influence, then it is tangible, thus natural), then science can increase its knowledge progressing towards increasing reliability of the universe. The only things that are left are things that have no influence or meaning - which science wouldn't touch, but are inherently not spiritual/etc.
That's fine and dandy - as a system. But that isn't the human component. It isn't what bonds societies in common belief, it isn't how we process information or make decisions... And people change science into the human mindset. Science, in that sense, is similar to religion because it requires faith in the knowledge we have accumulated. But the validity of that knowledge is what matters - and titles don't matter. An engineer three thousand+ years ago experimented and worked out math to build the pyramids, arches and so forth... and people built on it. It doesn't matter if they were part of the religious caste, and were passed down their knowledge as if it were 'from God', or from the sacred scrolls... it still exists. And we don't do it differently now - that's exactly what textbooks in universities are.
And I don't see anything wrong with this. It's the most efficient way I can think of having an organic learning system. And the knowledge that comes from the systems is a social good, so to speak. I can generally peer down the history of what allowed my calc derivatives to be 'discovered', but it's only after, when I realise how much of my other courses depended on it (last week, it was realising how chain-management was related, a real shock to me) that I realised I do have to take a lot of what I learn as faith.
And if the knowledge there lets us improve along one dimension - say, technology (ie: standard of living) - it's easy to see how other systems could play into the big picture too, like social coherency.
Just as science is inherently conflictive (if everyone agreed, there would be no 'science' system), religion can be inherently cohesive (if everyone agrees.)
[/rambling]
Just thinking out loud, for most of it.