Yeah, players being invisible is quite common now, especially after teleporting and respawning. Notch updated the player position code but it still needs work.
For now, reconnecting fixes this.
Also, there's light bugs causing super dark shadows, and other stuff. I don't expect a new update or hotfix soon though, there's alot of code to add and rewrite to make things work.
I'll expect one somewhere mid december I think.
But I said this before, SMP finally being added makes up for all of that! It's what I've been waiting for since I first played MC! It's awesome teaming up together to find and share resources, building a shelter before the sun sets, exploring cave after cave together. It's one epic adventure!