Lathe threading mistakes I've made plenty. The only mistake I've made using a die and TAT is threading too far. It didn't effect anything and the FSB covered the extra thread, but it doesn't look professional. Other mistakes I can see happen is not using a TAT, not ensuring that your barrel OD is the correct size for threading, if you have a split die trying to start the thread with it in the tightest position, not using any/enough cutting fluid, not backing off the die every quarter turn or so, not clearing out the chips if it gets too impacted, not using a die wrench and instead using something like vise grips, or not starting the die on the correct side. Probably the biggest one if trying to cut a left hand thread is turning the die the wrong way. I'm sure there's more, but those are things I can think of off the top of my head.
ETA: Just looked up the kit. Seems it comes with everything you need to not mess anything up. Make sure you really use that Tap Magic (love that stuff) and make sure you use the TAT (thread alignment tool) at least until you have a quarter inch of thread cut (or as close as you can get to that).