I think the underlying plot of it is unbelievable and there are so many issues with it, but I love it anyway.
Like, if the doctor can see everything that happened and will happen and that could happen, then why are they ever surprised? Wouldn't he just be like a robot carrying out the actions that he sees? Also, why would, for instance, Rose say her mother would have seen her with her father as he died because she went back in time to change the past, but later in the episode at the hospital (first episode, second new season) that woman played the video of herself at that party but it didn't show her with herself in that man's body. That's such a HUGE inconsistency. The only time travel that makes sense to me that I've ever read or seen was Jo Rowling's in Harry Potter and the Prizoner of Azkaban.