Just tried to do this HA (did it earlier with slightly different tasks) https://prnt.sc/uci3kw the "a sickly test subject" will not accept "healing salve" = can't finish the mission
Not a bug. You don't give it to them, you heal them. loot "Healing Salve", and right-click them on the gnome test subjects.
Usually the task will tell you, though sometimes it can still be hard to tell what action is required, usually items without a spell shown on them when you inspect are hand ins or self-activate while stuff with a triggered effect/cast time will need you to click them with a specified target or location being needed. A few need to be clicked even though they have no visible effect showing on them but they are less common.