Yes, the horribly corrupt Iraqi army. The US should have split the country up right from the start, as even had they retained the core of Saddam's military, a move advocated by many they'd in turn just have tried to continue to oppress the Shia and the Kurds and all you might have today would be a different Shia flavoured uprising and the Kurds would still have been the Kurds.
Well with the losses my mc's squad took in the game I never did apply for new recruits so as not to undermine discipline, morale and readiness, but yes there would be a limit to which that can be stretched. I believe in-game my mc's unit did well-enough at around 80% strength. Still I'd get a bit worried if we drop below two-thirds.
Hmmm....I heard that whenever the budget allows, which it hasn't for quite a while now our own military likes to over-recruit by about 10 to 20 percent, presumably in order to better be able to absorb losses should it come to a fight.