In fact to create weapons-grade Pu, you need to remove as much Pu-238 as you can, because if Pu-238 is contaminating your Pu, its high fission rate means the bomb explodes too early in the implosion process.
Right. Pu238 alpha decay is aneutronic so it doesn't contribute to a chain reaction. However heating from too much Pu238 (or more importantly, Pu240) would be a heat removal/thermal challenge.