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Next-generation spectroscopic surveys will map the large-scale structure of the observable universe, using emission line galaxies as tracers. While each survey will map the sky with a specific emission line, interloping emission lines can masquerade as the survey's intended emission line at different redshifts. Interloping lines from galaxies that are not removed can contaminate the power spectrum measurement, mixing correlations from various redshifts and diluting the true signal. We assess the potential for power spectrum contamination, finding that an interloper fraction worse than 0.2% could bias power spectrum measurements for future surveys by more than 10% of statistical errors, while also biasing power spectrum inferences. We also construct a formalism for predicting cosmological parameter measurement bias, demonstrating that a 0.15%-0.3% interloper fraction could bias the growth rate by more than 10% of the error, which can affect constraints on gravity from upcoming surveys. We use the COSMOS Mock Catalog (CMC), with the emission lines rescaled to better reproduce recent data, to predict potential interloper fractions for the Prime Focus Spectrograph (PFS) and the Wide-Field InfraRed Survey Telescope (WFIRST). We find that secondary line identification, or confirming galaxy redshifts by finding correlated emission lines, can remove interlopers for PFS. For WFIRST, we use the CMC to predict that the 0.2% target can be reached for the WFIRST Ha survey, but sensitive optical and near-infrared photometry will be required. For the WFIRST [OIII] survey, the predicted interloper fractions reach several percent and their effects will have to be estimated and removed statistically (e.g., with deep training samples). These results are optimistic as the CMC does not capture the full set of correlations of galaxy properties in the real Universe, and they do not include blending effects. Mitigating interloper contamination will be crucial to the next generation of emission line surveys. [ABSTRACT FROM AUTHOR]