We are monitoring the biosphere, but are not doing a very good job at organizing this information.
This is an overview of open biosphere monitoring platforms from citizen science projects to earth observations from space.
Many platforms allow recording of species observations, This photo will eventually link to a list that gives an overview of them
An increasing number of platforms allow people to share specific observed attributes of species, such as bird songs. In the near future, you will find an overview here.
The sharing of genetic information through centralized databases has been emphasized from early on in the rapid development of genetic sequencing. In the near future, you will find an overview here.
There are hundreds of biosphere observing satellites orbiting the planet and many of their observations can be found on the web. An overview of them will appear here.