How are they anti-military?
Of course any opinion as to their representations of military, such as the convoys and shipboard discipline forgets that this isn't our military, and things would likely be done differently in a completely different society. And add to that the fact that the Galactica was the dregs of the fleet, and that the Pegasus was run by a wannabe Col Kurtz.
Computers - how are Cylons infiltrating the systems? Just because the comps are "networked" shouldn't be a threat if there is no external access - shouldn't be hard to control. What, do they all have wireless links just waiting for Cylons to sync up? Like most writers, they're clueless; computers, and esp. things like computer "viruses" etc. are magic.
I don't think Galactica was run by the dregs; maybe by the old guys nearing retirement. Gaeta ain't dregs by any measure. Don't think Chief or the deck crew were, either. Dunno 'bout D, but she doesn't seem like it either. (One thing, of many, I like about BSG is enlisted and support personnel get some face time!) Starbuck is a problem child, but they would have run her through some schools to fix her or kicked her butt out. Apollo is okay if you keep him busy and away from politicians.
Also, I keep forgetting - impulse control seems to be seriously lacking in the Colonial Military. Spent four years in the army and NEVER saw anybody hit someone outside of HtH training. Or throw a tantrum.
Admiral Caine was an example of "anti-military" bias. In decent militaries, "Col. Kurtz" types are pretty rare, to put it mildly. The seldom become Admirals. You don't want 'em orbiting YOUR planet with that much firepower...
Also, most Admirals know quite well that no winning army in history would ever pass inspection... Patton might be an exception. Other stuff include various riots (like the coffee 'massacre' or the guy holding a gun a Tigh's head 'cause he was upset about the massacre).
I only have a few militaries to compare to, but the US is probably the most liberal one that can be taken seriously (can you imagine basing the Colonial forces on, say, the Dutch military with long hair and unions?). Most others would be much tougher...