Once on each of your turns as a bonus action, you can mentally command the servant to move up to 15 feet and interact with an object. The servant can perform simple tasks that a human servant could do, such as fetching things, cleaning, mending, folding clothes, lighting fires, serving food, and pouring wine. Once you give the command, the servant performs the task to the best of its ability until it completes the task, then waits for your next command.
(PHB p. 284)
What happens if the Unseen Servant e.g. tries to steal gold out of a pocket? Or if he is commanded to pick a lock? I would consider those as "simple tasks that a human servant could do".
Can an Unseen Servant do actions that require ability checks (apart from attacking, which is explicitely prohibited) and if yes, does the caster add his relevant modifier and proficiency bonus?