What would it be then, for rules to lack verisimilitude? Contain contradictions? Say in one place that magic armor is half the weight of normal armor and in another that it is virtually weightless?
Yes, that would count.
Contain multiple discrete subsystems?
Not necessarily an issue, as not everything in the world works the same - playing tennis is not much like research chemistry. Different subsystems can be okay.
Like overbearing and pummeling and turning undead all use different mechanics?
Well, here's where we sometimes get a problem, and sometimes not.
I would expect pummeling to be only slightly different from hitting a person with a sword. Overbearing a target yet more different, and maybe needs a bit of a different mechanic, maybe not - it'd depend on the specifics. The 1e systems for this - yes, a bit of verisimilitude problem.
Unless turning undead is largely comprised of beating my fist against the vampire's face, I don't think using a different mechanic for it is problematic.

I don't think that's what people mean when they talk about a ruleset lacking verisimilitude. They are referring to a contradiction in what the rules say and in what they perceive as the reality of the game world.
It seems to me that the rules *define* the reality of the game world. If your perception doesn't match, there are two basic possibilities I see:
1) The rules are not written well, so that you cannot gain an accurate perception of their implications - this is an issue of lack of clarity, not lack of verisimilitude.
2) Something other than the rules is giving you your perception of the world. It is this other thing, then, that lacks verisimilitude.
Perhaps there is a chicken-and-egg thing going here - which comes first, the rules, or the perception of the world they represent?