The 24 hour weighted average price (VWAP) showing on Mt. Gox.com website is what gets used for settlement. [Edit: The 24 hour VWAP at the "largest exchange" is what gets used for settlement, but that just happens to be Mt. Gox, for now.]

The settlement occurs at the clearing time (20:00 UTC) on the settlement date (e.g., April 14th, 2012 for BUJ3).   That's from the contract, combined with general instructions from the page describing how ICBIT futures work.  

As far as that number being obtained from a "screen shot", every trade at Mt. Gox is logged and is publicly available.  From that data, you can calculate the 24 hour VWAP yourself.  If you have reason to believe the VWAP grabbed at the time of settlement (20:00 UTC) is not accurate please raise that concern publicly as that would be a problem (as many merchants, traders, and others use that metric from Mt. Gox as well, ... though nobody else has raised concern about its accuracy.)

Of course, there needs to be just "one price" used for settlement at ICBIT.  And that price needs to be known at the time of that settlement day's clearing.   If you believe the use of this 24 hour VWAP is problematic, or whatever issue you seem to have with this metric being used, please clearly state your argument.   If I recollect it seems that you are saying you believe the 24 hour metric at 00:00 UTC (four hours after clearing) should be the metric used and not the number that existed at the time of the 20:00 clearing.  Am I understanding correctly where you believe the issue lies?  If not, please clearly describe what exactly is the particular problem you see with using the 24 hour VWAP that exists at the time settlement (& daily clearing) occurs.