Why when traveling abroad, at an exchange window, do I get a different rate for my USD depending on the series of the bill?

No. But you will get different rates from different vendors.

It is vaguely possible that they're not giving as good a rate on the older bills simply because of the possibility of them being counterfeit (which, overseas, is probably 50/50 and that's NOT an exaggeration.)

I've never heard of it, but I've not exchanged much money overseas either, just trying to come up with a possibility.

Yes in certain countries, smaller denominations are not as welcome, especially with smaller exchanges. Usually 50 to 100 denominations are preferred. Newer bills are also preferred even in the newest series. I think it is because they have a harder time converting the more used/abused bills to newer crisp bills. Bigger banks or international banks such as HSBC, Citi should have no problems giving you exchanges in whatever denominations you have. I would avoid local banks as they are a hassle to deal with. The caveats is that in the international banks and bigger banks you get the official market rates minus markups while in the smaller exchanges sometimes you get the prevailing market rates which could be much better than the official rates, especially in preferred currencies such as USD and Euro. The pound and lesser currencies are not as well received in the smaller exchanges.

question, when i was in madrid, used money machines, same as here in the states

i guess this is not common?