Background: Electroencephalography (EEG) provides a portable approach to assessing mild cognitive impairment (MCI) and early Alzheimer’s disease (AD), while sleep and autonomic signals may offer complementary physiological information. The validation quality of these computational biomarkers remains uncertain. Objective: To systematically evaluate signal-processing approaches, candidate biomarkers, computational models, and risk of bias in an EEG-centred evidence base for MCI and early AD, with complementary physiological studies considered as secondary evidence. Methods: Following PRISMA 2020 guidelines, we systematically reviewed 118 studies (2005–2025), comprising 113 direct EEG studies, two studies of polysomnography-derived sleep architecture, and three complementary non-EEG studies, and appraised risk of bias using a PROBAST-informed framework. Results: Recurring EEG findings included spectral slowing, reduced signal complexity, altered event-related potentials, and disrupted functional connectivity. Across 120 extracted performance rows, the median reported accuracy was 93.41%, and values above 95% were common. The proportion classified as High overall risk ranged from 38.1% to 69.5% across operational sample-size thresholds and was 22.0% when sample size was excluded. Twenty-two studies were at high risk of data leakage, only one reported external validation, and longitudinal evidence remained limited (9 studies; none used time-to-event modelling). Conclusions: The EEG-centred literature presents a performance paradox: high reported accuracy coexists with data-leakage concerns, limited external validation, and little longitudinal evidence. Future studies should use design-specific sample-size planning, strict subject-level separation, external validation, and longitudinal outcome modelling to establish clinically reliable computational biomarkers.