It's a tough question to quantify. I am entering a physical chemistry program. I'll most likely be doing theory (analytical theory, not computational simulations).
According to my coursework, I am knowledgeable in classical mechanics, physical chemistry, quantum mechanics, thermodynamics, statistical mechanics, spectroscopy, computational chemistry and inorganic chemistry, plus some stuff I am forgetting (not e&m, my big gap).
More personally, I feel I only have a good grasp of thermodynamics, quantum mechanics and stat mech at the undergraduate level. Those are the areas I feel very comfortable self studying, working out problems, filling in gaps, etc.
I am familiar with a lot more topics so when people talk about broadening in spectroscopy, or spin-boson model or lie algrebras, I can follow the terminology without getting lost but I am not particularly comfortable working on those areas by myself.
My math background is solid for a chemistry or physics major. I have a very good background in math, I've taken tons of courses BUT I am not particularly great at math so there are many people with lesser backgrounds who are more capable.