Probably the most obvious (and simple) way in which hashtags could be employed for advertising purposes on Facebook is to promote them in a similar way to the current promoted/sponsored posts.
Say a company is running a competition. They could promote their hashtag, #suchandsuchcomp, in posts that would appear in the newsfeed. How is that different to the current system of paid promotion? Well, clicking on the hashtag will reveal anyone using it in conversation, therefore providing a great tracking feature for advertisers and making it easier for users to find all associated info.
More importantly though, it means being able to tap into a previously untouched group who may not have liked the brand or have friends who like it, without the impersonality of the ‘old’ style promoted post.