Sophie Kaczynski's name should really be Zofia Kaczynska. The form 'Sophie' does not exist in Polish, and because Slavic surnames ending in '-ski' are grammatically considered adjectives, Zofia's surname should be the feminine form 'Kaczynska'. (In mitigation, the character may have dropped 'Zofia' in favor of the more English-sounding 'Sophie', but this doesn't explain the faulty surname.)
Oleg only wears a singlet on his torso when cooking in the kitchen of Han's diner. Dressing in this way would violate food hygiene regulations, which require cooks, chefs, and kitchen hands to be adequately covered in order to prevent hair and sweat from contaminating the food and beverages, however the quality, hygiene, freshness of the food, and overall cleanliness of the diner (or lack thereof of any of that) has been a running gag throughout the series.
Both Max and Caroline are seen wearing high heels while working in the diner. Servers wear flats for comfort.
The Season 1 episode 5 titled "And the '90s Horse Party" reveals that Max has a student-loan debt. The Season 3 episode 24, "And the First Degree" reveals that she couldn't possibly have that because she never graduated high school.