Good old Martha taught us that rather than buying those ridiculously expensive anti-slip mats for a rug, just turn it over and run a few lines of acrylic-latex caulk every 6 inches or so. Let dry and flip over and your rug wont be going anywhere!
Hang pictures without the trial and error: 1. Trace pictures onto brown kraft paper and cut out. Label each of the papers with a description of the picture or a corresponding number. 2. Using blue painter's tape (which won't pull up wall paint), tape the papers to the wall. Experiment with arrangements until you have one you like. 3. Install picture-hanging hardware directly through the paper. Pull paper away and hang pictures one by one.