The continuous time-tagging of photon arrival times for high count rate sources is necessary for applications such as optical communications, quantum key encryption, and astronomical measurements. Detection of Hanbury- Brown Twiss photon correlations from thermal sources such as stars requires a combination of high dynamic range, long integration times and low systematics in the photon detection and time tagging system. The continuous nature of the measurements and the need for highly accurate timing resolution requires a customized time-to-digital converter (TDC). We used a custom built, two-channel, FPGA-based TDC to continuously time tag single photons with sub clock cycle timing resolution for correlation measurements. We used autocorrelation and cross-correlation measurement tools to constrain spurious systematic effects in the pulse count data as a function of system variables. These variables included, but were not limited to, incident photon count rate, incoming signal attenuation, and measurements of fixed signals. We present an overview of the results of these tests, the types of systematic effects that the results imply, and how those effects may be accounted for and corrected to levels below those required for photon correlation measurements.