What nutrients might I be deficient in when trying to lose weight?

Take a multivitamin. When on a calorie-restricted diet, it make sense to take a multivitamin supplement daily. Women who are menstruating may benefit from an iron supplement also.
Adaptogen, glutamine. For weight loss the basic protocol involves adaptogens to reset adrenals, carnitine to boost metabolism, glutamine to heal pancreas, b vitamins for gut. Depends on which metabolism is affected. Lets say your triglycerides are high - then you would need carnitine and b2, if cholesterol is high you would need b6 and pancreatic enzymes, if you have increased plaque in teeth then digestive enzymes.