The only issue I've had so far with my Silhouette is the cutting mats. It wasn't even a week before they lost their tackiness and my paper was shifting. Which is kinda a major pain since then you have to try again. But I think I've found a solution.
I just use my Elmer's permanent glue dot runner on the edges on the back side of the paper before putting it on my cutting mat. If I'm cutting a really large sheet of paper, I might run a little glue in the middle too. It works really well! Just make sure you pull off your paper as soon as you are done cutting. Otherwise the glue will adhere and you'll end scraping paper off your mat.
I just made a countdown calendar for our trip to Disney World, and if I didn't have the glue dots, I know my little circles and numbers would have been a mess!
I made sure to grab some Toy Story stickers so that we can cover up the numbers as we count down.