I've been pouring with a Lee Production pot since about 2005. Yeah, I get drips occasionally.
1) there's a screw on top of the handle assembly. That needs to be adjusted properly.
2) Use only clean alloy in your pot. Never use it for smelting. I have a hot plate and an old metal pot that I use for smelting. From there, I pour ingots and it is only clean ingots that go into my production pot.
3) Flux is your friend. It's amazing how flux gets the crud to lift off surfaces and gets it to float to the top. I'll have a drip problem, and I'll just re-flux and it's magic.
4) The type of flux you're using is important. I use paraffin for a final flux to get things ready to pour, but I use (of all things) dried oak leaves for getting the bottom spigot ready for pouring. Some folks use sawdust. I just have plenty of oak trees in the yard. Swishing crumbled leaves into the pour usually does the trick for me.
5) Temperature. If I'm doing soft lead, I run it up all the way until things melt and then knock it back to about 8 to pour. Too cold and it won't flow right. Too hot, and I'll get drips.
I usually don't leave anything in the pot when I'm done. I drain the pot into a ingot mold and then unplug the unit and overturn it onto a flat roc and give it a good rap. Whatever comes out at the end is laden with dross. I save it and recycle that into my next smelt, but it never goes back into the production pot as-is.