Honestly, the HTML that word churns out is worse than dog puke. Use notepad.
That said, here goes.
Tables: I picked up a simple HTML example document from
here. It has a few tables. Loaded it into calibre, converted it to epub. Loaded onto reader.
Looks great; tables work just fine for me. A horizontal rule example from
this page worked fine too.
I'm not sure what you are after with the lists, do you mean a nested one
like this (worked fine as epub on the reader)? I can't get all bullet types to show but the ones
here work fine.