Yup, there are always things around that babies/toddlers/children shouldn't touch. Our nursery makes things as safe as they can, and then has rules about what is off limits.
In the baby room babies (up to 2 years) are not allowed near the highchairs at the side of the room or near the doors or to play with sockets (!). They're told 'no, come away from the xxx' and moved away.
In the toddler room there is a big cupboard where toys/craft stuff are kept, doors again, sockets again, and adult chairs are off limits too.
By the time they're in the preschool room, there are taps, scissors (safety ones, but still restricted access), window catches, paints, everyone's bags/coats/wellies, all sorts really, that the kids are not allowed to touch without asking. The kids are generally very good at understanding what's off limits because they hear the leaders consistently repeating to any child that touches something inappropriate that it is not allowed because ...
On the subject of other people's belongings, I have always steered my kids away unless the owner is there. They want or have wanted to touch all sorts of stuff - buggies, bikes, scooters, motorbikes, cars, shopping in baskets/trollies, handbags/changing bags .... the list is endless. It all gets an age appropriate 'no, it's not ours so we don't touch' or similar from me. I wouldn't rootle through someone else's buggy/car/handbag/trolley, so they need to learn not to as well!
One final point - if you're in the uk, socket covers are almost always not needed, and actually make the sockets less safe (unless they cover the whole block, not just the three holes). There is info here - www.fatallyflawed.org.uk