These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Songbird is by far the most popular member and has been involved in every incarnation of the Thunderbolts, as a member or not. She is usually the represented member if the Thunderbolts are mentioned and quite a few fans even requested that she make the cut for Marvel vs. Capcom 3.
Amusingly, these two breakout characters were chosen by Busiek for opposite reasons: he wanted to use Screaming Mimi because she was a blank slate that he could do anything with, but he wanted Moonstone because she was too well-defined and awesome a character to pass up. While neither is really a mainstream A-list character, the series put both of them on the map.
It Was His Sled: The Thunderbolts were actually the Masters of Evil. Despite this, the initial twist still works.
The name and powers came from a fan who won a contest in Wizard Magazine. Kurt Busiek developed his alter ego as a young African-American boy, presumably to bring some diversity to the team (which at that point had only one non-white member, Jolt).
The Woobie: Troll has her moments, such as the downcast look on her face shortly after getting taunted by other prisoners, or her run-in with past!Songbird, who she hasn't figured out doesn't know her yet.
Unfortunate Implications: The first issue mostly consists of white people (Punisher, Elektra, Thunderbolt Ross, Venom) killing people darker than them (Africans, Afghanis, Italians). Whether Deadpool killing French mimes is a subversion or played straight is up for debate.