1. производить смотр
It's used in a military context. The expression means that soldiers stand in lines on the parade-ground (or another place for that) and their commander inspects them (how they look etc). So, performing this action is "производить смотр [войск]".
Also it can include a review of their warlike equipment (weapon, tanks, cannons etc) and warships. So, it's close to "review" or "parade" (in a military context). That's like "show of force" - soldiers must look properly, be brave, healthy etc.

Смотр войск перед парадом:

(The navy cadets and their commanders участвуют в смотре войск)

2. производить обыск
This one is used in a police context. "Обыск" means "search", like in "body search" = личный обыск. Also cops can "производить обыск" in houses, appartments, cars etc, when they try to find some evidences (= улики) of the crime.


3. Производить осмотр
That's close to the first one, but not that specific. It means "to perform a [visual] inspection" and can be used in different contexts. For example, a doctor "производит осмотр" of a boy: