In the list 'Mardi Gras', 'St. Patrick's Day', 'Independence Day', and 'Labor Day', the odd word out is 'St. Patrick's Day'.
Reasoning: Mardi Gras, Independence Day, and Labor Day are all public holidays celebrated in the United States. St. Patrick's Day is a cultural and religious celebration observed in several countries, but it is not a federal public holiday in the US in the same way the others are.