I'm watching the original series, and just finished episode 346 (Vicki's dream of being in Josette's room with Barnabas and Julia; Julia bringing flowers to Vicki and them wilting after Barnabas touches them). There isn't really anything plot wise that made me think of the Burton movie, but the overall tone--and in particular some of the actors' mannerisms--really struck me as being key to the essence of the movie. Just the whole weirdness of it all, and the melodrama mixed with humor. THIS must have been what Burton was after, and I think he did very well in that regard.
One other thing came to me: A major criticism of the movie is that Vicki drops out of it for an extended period of time. Well, part of what Burton said he wanted was to emulate the episodic, soap opera aspect of the show. And on the original show, characters would frequently disappear for several days, often even for weeks at a time. For instance, Carolyn just showed up today after being gone a long time.