Background: Monitoring nutritional status data in the adult population is extremely important to mediate their health status. Unfortunately, for Slovenia (2.1 million European Union citizens), data on the body composition status of the general adult population are currently rare or nonexistent in scientific journals. Furthermore, dietary intake was last assessed several years before the COVID-19 epidemic period. Methods: We randomly recruited 844 adult Slovenes from all regions of Slovenia. The primary aim of the cross-sectional study was to examine body composition status (using a medically approved electrical bioimpedance monitor) during the post-COVID-19 epidemic period. In addition, we assessed dietary intake (using a standardized food frequency questionnaire) and compared the obesity propensity for both sexes separately using the body mass index (BMI) and body fat percentage (FAT%) obesity classification of the World Health Organization. Results: Regarding BMI classification, 43% of the whole sample was overweight (28%) or obese (15%), and there were more older adults than adults (64% vs. 42%, p < 0.001). The average FAT% of adult females and males was 26.9% and 19.5% (p < 0.001), respectively, while for older adult females and males, it was 32.7% and 23% (p < 0.001). In addition, a comparison of the proportions of obese people between the two cut-off obesity classifications (BMI vs. FAT%) showed a significantly underestimated proportion of obese female participants based on BMI classification (13% vs. 17%, p = 0.005). In terms of the dietary intake of the assessed nutrients in comparison with the national dietary reference values for energy and nutrient intake, the participants, on average, had lower intake than the recommended values for carbohydrates, fiber, vitamins C, D and E (for males) and calcium, and higher intake than the recommended values for total fat, saturated fatty acids, cholesterol, sodium and chloride (for males). Conclusions: The results urgently call for the need to not only improve the overall national nutritional status but also for regular national monitoring of body composition and dietary intake statuses.