I LOVE plastic detail cookie cutters. If you don't want them, send them to me!
Here are my hints for making them work, as well as the old fashioned tin type with backs. I used to chill my dough before rolling and cutting, but I don't anymore. I chill after they are cut and on the tray before baking. I found that small detail parts of the dough were more likely to stick in the cutter with cold dough. Each cutter can be a little different though, if it doesn't work one way, I'll try another.
I roll 1/4" deep between a long folded over sheet of wax paper on a doughboard. After the dough is rolled, lift just the top section of wax paper. I use one of these to dust the dough very lightly with flour. http://www.amazon.com/RSVP-Endurance-Fine-Mesh-Shaker/dp/B0000CFPV9/ref=sr_1_5?ie=UTF8&qid=1316808127&sr=8-5
By not lifting the bottom section of the wax paper and flouring that side before cutting, the slight stickiness of the dough will help the cutout adhere to the wax paper as opposed to stuck in your cookie cutter when you lift it.
Press your cutter well into an an unrolled dough blob. That allows it to pick up just a bit of grease from the dough and the flour you next dip the cutter into will be more effective. Don't spray the cutter with PAM before dipping. That just makes a mess. 1/4" thick dough is just a little deep for some of these cutters, so what I do is put the cutter down one side at a time and use somewhat of a rolling motion toward the other side of the cutter. What this does is allow any excess dough height to kind of bloop out to the side.
Next I pull the wax paper with the cut cookie on it toward the edge of the counter. I pull the paper away and let the cut cookie gently fall onto my hand. Then I place the cookie on a tray with parchment to chill, and then bake.
If the dough does stick despite these efforts, I'll often just try again. With a little more grease from the dough and re-floured, the next time probably will work. Yes, they are more trouble than open cutters, but I like the designs enough to mess around with them.