Ordinary tap water certainly contains contaminants and impurities that are injurious to health and these will largely be removed by a reverse osmosis water filter. But the bad news is that in addition to the nasties they remove, they also do a sadly good job of removing minerals from the water that have positive health benefits.
How do we know that completely demineralized water is not a good idea? Well, it doesn't occur anywhere in nature, so this fact alone suggests that a commonsense interpretation is that water containing minerals is essential for life.
Not everyone is in total agreement that removing just about all of the mineral content from the water you drink is necessarily a bad thing. But, what is not in doubt is that you must supply your body with a comprehensive collection of minerals to maintain optimum health. Given this fact, it surely makes sense that you should be providing at least some of those minerals via the water that you drink on a daily basis.
Does reverse osmosis make water safe to drink? Sadly, the answer to this has to be no. The reason is that this process does not entirely remove synthetic chemicals that can be found in everyday tap water.
Are there other disadvantages to reverse osmosis? Well, becuase of its very strong filtering abilities, it leads to the wasting of a lot of water - because a significant volume of water is discarded along with the filtered impurities. This waste of water is not particularly good for the environment and can lead to you paying higher water bills.
Another more minor disadvantage of reverse osmosis water filters is that some of the ones that are designed for attaching to individual faucets externally can be unsightly.
All in all, although it is certainly a very good idea to get a home water filtration system there are just too many disadvantages of reverse osmosis for this to be an effective system.