Background: Cognitive impairment is a relevant problem in psychiatry and can be well assessed with a cross-diagnostic test such as the Screen for Cognitive Impairment in Psychiatry (SCIP). The aim of our pilot study is to assess cognitive impairment in acute psychiatric inpatients diagnosed with psychotic disorders, bipolar disorder and depression using the German version of the SCIP (SCIP-G). We also investigate whether cognitive dysfunction improves over the course of the inpatient treatment, where patients are offered a combination of pharmacological treatment and cognitive remediation. Methods: A total of 143 adult inpatients were included in the study. Cognitive testing was performed using two different forms of the SCIP-G. All patients received state-of-the-art pharmacotherapy and cognitive remediation using the COGPACKÒ software package version 6.06. Results: Based on the ICD-10 Criteria for Research, 54 patients were given an F2 diagnosis (schizophrenia and schizotypal and delusional disorders). Thirty-nine patients met the criteria for bipolar disorder (F30 and F31) and fifty for depression (F32 and F33). At baseline, a significant difference was observed between the SCIP total scores of the F2 and F32/33 patients (p < 0.001) and between the F2 and F30/31 groups (p = 0.022). At the second measurement time point, the SCIP total score showed significant improvement in all three groups (p < 0.001), and there was no statistically significant interaction between SCIP total score and diagnostic groups (p = 0.860). Conclusions: Cognitive dysfunction is present in psychiatric disorders and can be easily assessed during an inpatient hospital stay. In our sample, patients with a psychotic disorder were more cognitively impaired at baseline than patients with an affective disorder. Inpatient treatment, consisting of pharmacotherapy and cognitive remediation, improved cognitive deficits. Patients with psychotic disorders, bipolar disorder and depression showed similar improvements in cognitive performance.