How do I monitor power consumption?

As you surmised in your comment the limitation is not with the software but with your battery not reporting correctly.

To clarify these software tools below will only measure power consumption on laptops when running on battery. For desktop or server machines the only current solution is an electronic watt-meter that plugs into the mains socket.

Power Statistics

In Ubuntu Precise 12.04 there is a new power statistics history window. This can be accessed by clicking the battery item in the application indicator menu then selecting Latop Battery tab.

Powertop

As mentioned by the OP this program provides information on per process/device power usage.

Powerstat

Another alternative that measures process/device power usage is powerstat that was written for Ubuntu by Colin King. There is a detailed review of its features on hecticgeek.com.

It can be installed from the PPA: ppa:colin-king/powermanagement

You can have a look at PowerAPI (on github), which gives the power consumption at the process level on Linux. According to some experiments, it is more accurate than Powertop.

Have a look at s-tui: https://amanusk.github.io/s-tui/. Runs in the terminal, shows you the parameters pertinent to the CPU.