Off the top of my head (some of this may count as Phys Chem, but is necessary to proper understanding of Inorg Chem):
Atomic structure, electron configurations, Aufbau principle, periodic table. Periodic trends in properties.
Chemical bonding; ionic, covalent. Concepts of valency: oxidation state and coordination number. VSEPR and MO theories.
Basic chemical thermodynamics & kinetics.
Symmetry & group theory; spectroscopy. Basics of crystallography, common crystal structures.
Electrochemistry: electrode potentials, electrochemical series.
Transition metal coordination chemistry, d configurations, low/high spin, spectrochemical series.
Basics of organometallic chemistry (does that count as Inorg Chem these days?)
Basics of common analytical techniques e.g. spectroscopy, chromatography.
Plus a fair bit of simple factual what-reacts-with-what chemistry - properties of common elements, simple compounds e.g. oxides, halides, basic aqueous chemistry, typical oxidation states.
And enough maths to do the above properly (including basic statistical analysis of data).