Bottom pour casting pot maintenance ?

Good question. I wondered about that too. I always drain the pot down to about 1”. Scrape the sides and around the pour hole and use a paper clip to clean the hole before shutting the pot off. I figured it was best, or at least faster for the pot to warm up new lead if there was a little left in the bottom. Besides, I drain the lead and put it in moulds labeled as to the type of mix I have in it. I also leave a catch pan under the pour hole while the pot it heating. I have had the hole leak and pour out a big puddle on my work bench. 
 
Smelt and clean your lead good before putting it in the Lee pot and you shouldn't have a problem. I will drain my pot every few years and scrap out the bottom but it's mostly something I do when I've about cast all the lead out of the pot and I'm done casting for a while. Big thing with the Lee pot is turn the valve stem every once in a while to clean out the seat so the dripping is kept to a minimum, I don't remember if the Lee 10 pound pots valve stem can be turned but I know the valve stem on the 30 pound rotates, been a while since I cast muzzy bullets out of my 10 pound.

I've cast over 20,000 pistol and rifle bullets along with 10,000 pieces of buck type shot without very many Lee pot issues. I mostly use the Lee 20 pound bottom pour pot for metallic cartridge bullets and the Lee 10 pound for muzzy bullets.