I am now an expert of sorts in coring processes, and I would characterize the current use of ice cores as an appropriate measure of past CO2 levels as flawed. Principally, the two arguments I would outline are:
1) the measurements do not reflect the transport of CO2 into and out of the ice cores. Do not give me this crap about ice not being permeable -- it just isn't true. It also doesn't account for any freeze-thaw cycles or sub-surface water flow. Basically, the history associated with the ice core is not correctly reflected in the calculations. Correct history would require in-depth modeling of thermal and flow conditions -- not something that the "climate scientists" are in any way trained to do correctly (I've learned this first-hand was well). That thermal/flow model should have multiple sources of independent data to feed into it as well, in order to properly "history-match" the ice core in question. I doubt that a historymatched would be "unique" anyway -- so basically the true solution to the historical CO2 levels based on even well-modeled data would likely not be the right solution.
2) the process of coring and extracting cores seriously calls into question the results, particularly for accurately determining a GAS concentration in a sample. My strong suspicion is that historical values are underestimated (and increasingly so with increasing depth) because they do not account for pressure differences during the coring/extraction process. Basically -- by the time you get it to the surface, or even when you dislodge it from the ice sheet, you've likely lost a bunch of gas by expansion and pressure drop.
BOTH of these flaws would lead one to believe that CO2 levels collected in older ice core samples UNDERESTIMATE the actual levels at those times.