I only have experience with two shared hosts. The other one is a cPanel/Fantastico host. I think the DreamHost panel and setup makes it easier to deal with multiple domains and subdomains. It's just more intuitive to me.
I'm not an SEO expert, so I'll let others answer this.
What sort of problems might you anticipate? I use two hosts myself and have subdomains hosted on one where the domain is hosted on the other. I don't do any cross-marketing.
I'm not sure how Google identifies separate entities. If it's by IP, you mostly end up with the same IP address - though I had two or three IP addresses back before I went for the DreamHost PS service.
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