Dee was too whiny for me. She always had reasons to complain and to whine about. But I really loved the way she exited the series. She had no more hope that she couldn't take it anymore. Awesome scene. I wished Star Trek could be more like nuBSG because I gotta admit, nuBSG is the best sci-fi-series ever IMHO.
Interesting, because I hated the way she left the show. I thought it was a cold send off, after underusing or mishandling her character to have her kill herself off. I don't think the writers knew what to with her after Billy and especially after her marriage to Apollo and perhaps went for a 'shocking' ending. I just saw it more as the conclusion of writer disinterest in Dualla's character.
Overall I never thought she was whiny. I thought she was put in poorly conceived relationships. Apollo seemed a more logical choice to me than Billy did, but with Apollo she sort of came off as an other woman even though she was his wife. Perhaps it was a way for the writers to try to do something with her character, but I thought it was the wrong way to go. Some of her best stuff came in Season 1 with Adama, and I wished they had continued developing that relationship, with him being able to talk to her, open up to her in a way he really wasn't able to do with Apollo, Starbuck, and even Roslin.
It sucks that perhaps the best Dualla storyline came out of the BSG comics of that time, the one about the Returners. I wish they had adapted that for the TV show, even though I'm not sure how that would've jibed with the show later did with the Cylons.