Many bottled waters have an expiration date on them. This is not because they will go bad, but because some places have laws that say every drink has to have an expiration date. Even if you don’t live in such a place, the bottling company wants to be able to sell the water in those places, so they print a date on the bottle.
It may also help their sales if people think they have to buy new bottles of water instead of drinking the older ones in the back of the refrigerator.
Plastic bottles will gradually release volatile molecules from the plastic. Most of these will escape into the air, but some of them will get into the water. It is unlikely that you would be able to taste them in the water, however, and it is not clear that they would accumulate over time instead of being reabsorbed in the plastic once they reach equilibrium levels in the water. Glass bottles don’t have volatile molecules to leach into the water.
An unopened bottle will not allow algae or bacteria to grow in it. Once the bottle has been opened, however, it is possible that algae spores could make their way into it, and with enough sunlight, you could get a green film on the inside of the bottle.