[YeGoblynQueenne]

You're talking about the difference between the percentages of applicants of each sex that were admitted. I tabulate:

                  Men              Women              % Difference
    Department Applied  Admitted Applied  Admitted    Men     Women
    A          [825]    62%      108      [82%]               +20%
    B          [560]    63%      25       [68%]               +5%
    C          325      [37%]    [593]    34%         +3%
    D          [417]    33%      375      [35%]               +2%
    E          191      [28%]    [393]    24%         +4%
    F          [373]    6%       341      [7%]                +1%

So, there's a 20% difference for one department that is a clear outlier and then everything is within a couple of percentiles of difference. In fact, the average difference is higher for men (3.5) than for women (2.666) ignoring the outlier, since it's an outlier.

However, I'm really not sure that taking the difference between proportions of different wholes is meaningful. The numbers don't add up to 100, so what does the difference mean, exactly?

I don't know what "a stats 95 confidence style" is, or how it is related to a margin of error, so please do that calculation and post your results.