SDSS-IV MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) is the largest integral-field unit (IFU) spectroscopy survey to date, aiming to observe a statistically representative sample of 10,000 low-redshift galaxies. In this paper, we study the reliability of the emission-line fluxes and kinematic properties derived by the MaNGA Data Analysis Pipeline (DAP). We describe the algorithmic choices made in the DAP with regards to measuring emission-line properties, and the effect of our adopted strategy of simultaneously fitting the continuum and line emission. The effects of random errors are quantified by studying various fit-quality metrics, idealized recovery simulations, and repeat observations. This analysis demonstrates that the emission lines are well fit in the vast majority of the MaNGA data set and the derived fluxes and errors are statistically robust. The systematic uncertainty on emission-line properties introduced by the choice of continuum templates is also discussed. In particular, we test the effect of using different stellar libraries and simple stellar-population models on the derived emission-line fluxes and the effect of introducing different tying prescriptions for the emission-line kinematics. We show that these effects can generate large (>0.2 dex) discrepancies at low signal-to-noise ratio and for lines with low equivalent width (EW); however, the combined effect is noticeable even for Hα EW > 6 Å. We provide suggestions for optimal use of the data provided by SDSS data release 15 and propose refinements on the DAP for future MaNGA data releases.