Logo link issue aside, I'd love to host my company blog on Tumblr but have heard bad things about the SEO factor of Tumblr sites, even if you use your own blog.company.com subdomain. I have no empirical evidence of this, but anecdotally it appears to be true, so I'v been deterred.
I heard from discussions on SEOMoz blog that hosting on Tumblr doesn't give your domain the "SEO juice", but I don't actually know what that means. Perhaps your domain isn't marked as valuable when your popular posts are not hosted on your primary site. However, when your posts do get popular, they drive just as much traffic to your blog. They way I see it, it's your job to convert them over to the site itself. The "juice" value aside, Tumblr is so fast to setup that it was definitely worth it for us.
IIUC it's just that foo.com blog.foo.com do not count as exactly the same domain, so whatever bit of increased value a backlink gives to you gets split between the two domains rather than go to the same.
If the blog is under foo.com/blog, OTOH, all the link juice goes to the same domain.
