If someone set up a bowl of potion that is used to catch fruit flies, can one move it from one corner of the counter to another to be closer to the flies?

That would be similar to placing a trap on Shabbos which is forbidden.

Additionally, the trap itself is Muktza and can not be moved for this purpose.

ראה שו”ע אדה”ז שטז, ו. והוי ככלי שמלאכתו לאיסור.