Sorry for the delay; I was on a trip last week and the result is some new and important responsibilities -- hence I'm going to be posting VERY intermittently.
There's already a link in this thread that takes on the paper. But taking the long, big-picture view, there are probably hundreds of papers with data from ice cores around the world (particularly both poles) that all show the same patterns of CO2 increase over time. All subject to the same errors? Not likely. Plus, the layers in the cores are dated with ash from known volcanic eruptions, supporting the time trends of the gas. And the Law Dome and Siple Dome curves dovetail right into the instrumental record.
Here's a figure that puts into some perspective.
There are still some points on which it is possible to be skeptical on this issue (though being me, I don't recommend it as a strategy for long-term success, if one is actually trying to be correct about the issue). But questioning the validity of the CO2 concentrations in ice core bubbles is not a tenable position, at all.