In My Opinion...

Twilight should have been a television series, not a two hour movie. Building a devoted relationship such as Bella and Edward's takes time. Even in the book their experiences coupled with the level of their devotion was hard to swallow, but the movie lacked an emotional connection between the characters that really needed it. There was little time to see their relationship build at all, one second he hates her before you know it he's trying to tell her not to be his friend, and then she has figured out what he is and suddenly they are completely devoted to each other. Vertigo is an apt word to describe the experience. A television series would allow time for each of these things to sink in, you have a week to feel Bella's frustration before Edward comes back and frustrates her even more. You have time to put the puzzle pieces together with Bella. You'd sit and ponder the pros and cons with Bella when she is trying to decide what she is going to do when she finds out what Edward is. That part of the book is quick and even with the invincibility that comes with being a teenager, you would hope that she would think longer about it before accepting it.
The medium of a television series would allow the development of Edward's inner conflict between what he was and what he wanted to be. There are hints of it in the books, and even more in the section of Midnight Sun that was published online. Understanding that tension brings certain events into clearer focus. The other characters, which were not really developed could have also had their time in the spotlight. It adds depth to Bella's desire to want to be a part of the family, when you know what the family is like. An entire forty-five minute episode, hour if you include commercials, could have been devoted just to Carlisle's back story. The only exposure to the family the movie offered was them trying to fix dinner for Bella, a baseball game, and brief exposure while they were trying to save Bella from James. Once again, these relationships lacked an emotional attachment.
The series also would allow for the development of the fine line that the Cullen's walk trying to be a part of the human world while hiding their secret. How could Dr. Cullen be a Doctor if he was a vampire? An explanation of that can't be found anywhere in the movie.
The special effects couldn't have been that difficult. All they did was jump high, run fast, lift heavy things, climb trees, and sparkle in the sun. The sun sparkling was a little strange, and hard to detect. Perhaps a more effective way of doing it could be found, or another reason thought of that the Cullen's couldn't be in the sunlight. Future episodes with the werewolves might be more difficult to swing, but movies have done stuff like that in the past. Transformations were tackled in the '80's and Alsan in Disney's "The Lion, the Witch and the Wardrobe" was well done, though perhaps not practical for a television series.
Edward's extra power wasn't even evident in the movie, Alice's was glanced over and Jasper's wasn't even mentioned that I recall. In the book these powers were used rather effectively and created a reliance, a binding force to keep the Cullen's together in addition to their vegetarian diets.
As for paying for it, there was already a following of die hard fans, proceeds from commercials and product placements would have not been hard to come by.
The difficulty would come from needing to add enough extra but not superfluous information to clarify confusing points in the story and unseen plot twists to gain new viewers and to keep devoted fans from getting bored. Such as Bella finally confronting her fear of loss. Yes, please make the poor girl grow. The set up and circumstances could be intensely interesting. There's got to be talent out there willing and able to conquer it and make it good.