Systematic biases in climate models hamper their direct use in impact studies and, as a consequence, many statistical bias adjustment methods have been developed to calibrate model outputs against observations. The application of these methods in a climate change context is problematic since there is no clear understanding on how these methods may affect key magnitudes, for example, the climate change signal or trend, under different sources of uncertainty. Two relevant sources of uncertainty, often overlooked, are the sensitivity to the observational reference used to calibrate the method and the effect of the resolution mismatch between model and observations (downscaling effect). In the present work, we assess the impact of these factors on the climate change signal of temperature and precipitation considering marginal, temporal and extreme aspects. We use eight standard and state‐of‐the‐art bias adjustment methods (spanning a variety of methods regarding their nature—empirical or parametric—, fitted parameters and trend‐preservation) for a case study in the Iberian Peninsula. The quantile trend‐preserving methods (namely quantile delta mapping (QDM), scaled distribution mapping (SDM) and the method from the third phase of ISIMIP‐ISIMIP3) preserve better the raw signals for the different indices and variables considered (not all preserved by construction). However, they rely largely on the reference dataset used for calibration, thus presenting a larger sensitivity to the observations, especially for precipitation intensity, spells and extreme indices. Thus, high‐quality observational datasets are essential for comprehensive analyses in larger (continental) domains. Similar conclusions hold for experiments carried out at high (approximately 20 km) and low (approximately 120 km) spatial resolutions.