Many of the exoplanets for which we can obtain the highest SNR transit spectra are tidally locked. The atmospheres on tidally-locked planets likely exhibit large differences between the day and night side of the planet, the poles, and the morning versus evening terminators. In this paper, we illustrate how the combined effects of aerosols and day-night temperature gradients shape transit spectra of tidally-locked exoplanets when full 3D structures are taken into account and evaluate the implications for retrievals of atmospheric properties. To do this, we have developed a new code, METIS, which can compute transit spectra for an arbitrary longitude-latitude-altitude grid of temperatures and pressures. Using METIS, we pair flexible treatments of clouds and hazes with simple parameterized day-night temperature gradients to compute transit spectra and perform retrieval experiments across a wide array of possible exoplanet atmospheric properties. Our key findings are that: (1) the presence of aerosols typically increases the effects of day-night temperature gradients on transit spectra; (2) ignoring day-night temperature gradients when attempting to perform Bayesian parameter estimation will still return biased results when aerosols are present, as has already been shown for clear atmospheres in the literature; (3) when a day-night temperature gradient is present and accounted for in the retrieval model, some transit spectra can provide sufficient information to constrain temperatures and the width of the transition from day to night. The presence of clouds and hazes can actually tighten such constraints, but also weaken constraints on metallicity. This paper represents a step towards the larger goal of developing models and theory of adequate complexity to match the superior quality data that will soon be available.