Digging partial plugs or if the find is reasonably shallow, the screwdriver method leaves little or no tell tale signs that you have been there. I really don't see any need to dig full plugs like you see a lot of on you tube, you can still dig a partial flap if the find is deeper. I am always bemused by people who dig huge plugs, then proceed to dismantle the plug only to find the coin was only 2" from the surface, completely unnecessary.
One of the reasons why I detect at night is not to hide what I am doing to the ground, but more to do with onlookers who take a disliking to detecting in their local park areas or oval surrounds, regardless of how well you dig the target, and repair any signs of being there. Unfortunately for us, some people have nothing better to do with their time, and are just looking for an excuse to get rid of us, regardless of how well we conduct ourselves.
Like I mentioned in a previous post, if you have kids starting out on detecting take them to the beach first to get their confidence up, and to get them in the habit of doing the right thing (taking rubbish with them, filling holes, pinpointing targets properly).
If you take inexperienced kids detecting at parks, give them the proper tools to do so (a decent coin recovery tool, not a shovel or pick). Also have them set their detectors on low sensitivity, so they only detect at or near surface targets, vs chasing every little junk target at depth. As you could imagine, this could possibly lead to holes all over the place. Only let them increase the depth when you are satisfied they can properly fill in holes, and identify targets to a satisfactory level.
ALWAYS use a pinpointer, hate seeing people dig huge holes, only to find the coin was in the side of the hole, 1" down!
Tot lots are a great place for kids to learn target ID's and signal responses without leaving too much of a mess, whilst actually having a chance of finding something decent.
Whilst there are some uneducated kids out there making a mess, there are probably just as many adults who deserve just as much blame, whether it be intentional, or unintentionally leaving holes or bad plugs.
If you can't dig proper plugs in the turf at home without leaving a mess, then you should not be attempting the same thing in public places.
Councils will always take the easiest and cheapest way out if they receive too many complaints, and that is to erect signage banning detecting vs managing the issue.