The problem here is that the society (with 'the') has quite a different meaning to society (without 'the').
If you're talking about all of humanity as a collective, then you're probably talking about society. In this case you're probably thinking about the whole of the human race at a particular time, usually around now. If problems are faced by society (without 'the'), then they are likely to be problems that all people face, either across an entire country, or possibly all over the world, and so in this case you need:
On the other hand if you're talking about a specific group of people who have some kind of shared set of specific interests then you need the society. For example in this list of academic 'societies', group members relate to each other because they share the same academic interests. Similarly, universities often have societies devoted to particular hobbies or interests. In this case you might be writing something like:
Notice that in this example, not only do we use 'the' to show that we are talking about a specific group, but we also use words to modify the word society so that our reader understands exactly which group we're talking about ('most popular', 'photographic').
So, be careful next time you use society! :)