Improving Star Cluster Age Estimates in PHANGS-HST Galaxies and the Impact on Cluster Demographics in NGC 628

A long-standing problem when deriving the physical properties of stellar populations is the degeneracy between age, reddening, and metallicity. When a single metallicity is used for all star clusters in a galaxy, this degeneracy can result in $`$catastrophic$'$ errors for old globular clusters. Typically, approximately 10 - 20 % of all clusters detected in spiral galaxies can have ages that are incorrect by a factor of ten or more. In this paper we present a pilot study for four galaxies (NGC 628, NGC 1433, NGC 1365, and NGC 3351) from the PHANGS-HST survey. We describe methods to correct the age-dating for old globular clusters, by first identifying candidates using their colors, and then reassigning ages and reddening based on a lower metallicity solution. We find that young $`$interlopers$'$ can be identified from their Halpha flux. CO (2-1) intensity or the presence of dust can also be used, but our tests show that they do not work as well. Improvements in the success fraction are possible at the $\sim$ 15 % level (reducing the fraction of catastrophic age-estimates from between 13 - 21 % to 3 - 8 %). A large fraction of the incorrectly age-dated globular clusters are systematically given ages around 100 Myr, polluting the younger populations as well. Incorrectly age-dated globular clusters significantly impact the observed cluster age distribution in NGC 628, which affects the physical interpretation of cluster disruption in this galaxy. For NGC 1365, we also demonstrate how to fix a second major age-dating problem, where very dusty young clusters with E(B-V) $>$ 1.5 mag are assigned old, globular-cluster like ages. Finally, we note the discovery of a dense population of $\sim$ 300 Myr clusters around the central region of NGC 1365. and discuss how this results naturally from the dynamics in a barred galaxy.