This thesis presents a few topics all related to the SNO+ experiment: improvements to the trigger system, measurements of backgrounds to a potential neutrinoless double beta decay ($0\nu\beta\beta$) signal, and a measurement of neutrino oscillation parameters using reactor antineutrinos. Two background analyses performed during the water and partial scintillator phases of SNO+ are presented. The first analysis measures the radioactive backgrounds from the external components of the detector in the SNO+ water phase. The second analysis investigates all backgrounds to a potential neutrinoless double beta decay signal in the SNO+ partial scintillator fill phase. Both analyses find backgrounds consistent with expectation. These background analyses also motivated improvements to the SNO+ trigger system. This includes additional trigger functionality and improvements minimizing the deadtime in the SNO+ trigger system. Finally, an analysis of reactor antineutrinos detected in 134.4 days of SNO+ data is presented. A fit of reactor antineutrino event candidates provides a measurement of $\Delta m^{2}{21} = 7.96^{+0.48}{-0.41} \times 10^{-5} \text{ eV}^2$ with local minima above and below the best fit value at $<2\sigma$ significance. Combining this result with the existing global constraint from KamLAND gives a new value of $\Delta m^{2}{21} = 7.59^{+0.18}{-0.17} \times 10^{-5} \text{ eV}^2$, slightly higher than the previous best fit. In addition, the flux of geoneutrinos is measured to be $64 \pm 44$ TNU, consistent with expectation. The future sensitivities of these measurements with additional data are also presented. It is concluded that SNO+ expects to reach the current sensitivity in its measurement of $\Delta m^{2}_{21}$ with $\sim$4-5 years of livetime.