Basically you need to look at two things:
- What you are hanging (how heavy, will it sway, is it a vertical load or does it have a horizontal component)
- What are you hanging it on (wallboard, plaster, old crappy plaster, stud wall, concrete wall, brick, stone, solid wood...)
Then you pick the right fastener at the intersection of these two.
Assuming you have a newer house, and are mostly hanging pictures, the old "nail into wallboard" will work okay. Just tilt it downward so the picture wire slides toward the wall, not toward the nailhead.
You can also use things like the 3M "command" strips, which work great if you follow the instructions and don't exceed the load. Don't be stingy with them.
Hanging heavier things like mirrors or glass picture frames, use the appropriate wall anchor for the wall, and/or nail or screw into the studs. With the right wall anchors, or rails or other structure attached to the studs, you can put an enormous load on the wall (tons) without problems.
If you have an old house like mine, don't even bother trying wall anchors into ancient crumbly plaster...find the studs. Hard-won lesson. ;)
Using a stud finder can be a bit of an art, so practice on a wall you don't care about. (Mark the edges of the stud, then drive a very fine nail into the wall board and see if you were right. Then, pull the nail and spackle the hole.) Also note that they read differently depending on what kind of wall it is.
This may be thinking outside the box, but there are other ways to display a picture rather than "hanging" them. Hopefully these inspire some solutions...
Have you considered using some sort of display easel like the one above instead?
Google Search: Photo Display Easel
Compression poles are also an interesting way to hang things without causing damage:
Or if you are more industrious, you can construct some sort of free standing (or leaning) panel to hang the picture from. A nicely framed section of painted drywall or other type of surface can make a nice accessory for the room. It can be made free standing or designed to lean up against the wall without causing any permanent damage.
Best Answer
Your walls ,because of the year you stated it was built are probably plaster. Plaster walls use lathing as an attachment under the plaster , but I don't see this as the problem you are encountering when securing accessories to the wall. I'm thinking that while drilling the wall in the bathroom: 1) you may have encountered a cast vent/waste pipe beneath the wall or 2) it could be a pipe or electrical wire protective plate that are installed when a wire or pipe are installed through a wall stud. Either of these would explain not being able to drill an opening. The first thing to be sure of is the material of the walls. Try to drill a small opening in an unobtrusive location ( down low and in a closet). You should see grainy course sand ejected as the bit pierces the wall.