I'm actually going to go on a limb and propose Liara is not all that inconsistent.
One of her defining characteristics are her strong will. She is the only one of the three LIs in the first game that can't have her opinins changed. You can paragon Ashley, you can renegade Kaidan, but try as you might, you can't change Liara's worldview. This serves her well while retreiving Shepard's body, on her hunt for Shadow Broker and throughout the whole third game. She is quite consistent in that aspect.
She is also shown to be resorcefoul. She admits, in the first game, that her theories aren't given the credence they would deserve because of her youth. I imagine that traslates into less funding by university and sponsors. And yet, she often performs digs on remote worlds. How did she get there? Sure, she is a daughter of influental matriarch, but her own mother and she are estranged and I imagine Benezia isn't pitching in a lot for what she sees as a folly of youth. Liara probably had to get most of the funding for her expeditions alone and I imagine that's not cheap. If she wasn't resorcefoul, she wouldn't be doing as much hands-on approach as she does.
I imagine that served her well when setting a bussiness for information brokering. I believe she also admits archeology and information brokering aren't all that different? Just the matter of finding the right information. She is a smart gal(seriously, a doctor at 50? That's what, fresh out of asari equivalent of high school), after the death of her mother she probably came into inheritance, so money shouldn't be a problem. As for training... I find it hard to believe there is college to which prospective brokers enlist. So yeah, she isn't stretching anything too much.
And before people start screaming bloody headcanon... yes, it is, to certain extent. But nothing too unbeliveable and nothing in the game canon opposes it, at least as far as I recall.
To me, she is quite consistent.