  Our understanding of the properties and demographics of exoplanets critically
relies on our ability to determine fundamental properties of their host stars.
The advent of Gaia and large spectroscopic surveys has now made it in principle
possible to infer properties of individual stars, including most exoplanet
hosts, to very high precision. However, we show that in practice, such analyses
are limited both by uncertainties in the fundamental scale, and by
uncertainties in our models of stellar evolution, even for stars similar to the
Sun. For example, we show that current uncertainties on measured
interferometric angular diameters and bolometric fluxes set a systematic
uncertainty floor of $\sim$2% in temperature, $\sim$2% in luminosity, and
$\sim$4% in radius. Comparisons between widely available model grids suggest
uncertainties of order $\sim$5% in mass and $\sim$20% in age for main sequence
and subgiant stars. While the radius uncertainties are roughly constant over
this range of stars, the model dependent uncertainties are a complex function
of luminosity, temperature, and metallicity. We provide open-source software
for approximating these uncertainties for individual targets, and discuss
strategies for reducing these uncertainties in the future.
