In test-negative design studies that use rapid tests to estimate influenza vaccine effectiveness (VE) a common concern is case/control misclassification due to imperfect test sensitivity and specificity. However, an imperfect test can also fail to exclude from the control group people that do not represent the source population, including people infected with other influenza types or other vaccine-preventable respiratory viruses for which vaccination status is correlated. We investigated these biases by comparing the effectiveness of seasonal 2023/24 influenza vaccination against influenza A and B based on PCR versus rapid test results, excluding controls who tested positive for SARS-CoV-2 or the other type of influenza. By PCR, VE against influenza A was 49% (95%CI 26-65%) after exclusion of PCR-confirmed influenza B and SARS-CoV-2 controls. Corresponding VE against influenza B was 65% (95%CI 35-81%). VE estimated by adjusting for COVID-19 vaccination status yielded similar estimates to the scenario that excluded SARS-CoV-2-positive controls. When case/control status and exclusions from test-negative controls were determined by rapid test, VE was reduced by 5-15 percentage points. Bias correction methods were able to reduce these discrepancies. When estimating VE from a test-negative study using rapid test results, methods to correct misclassification bias are recommended.