So my issue with being dishonest with its premise is pretty much along the lines of what mousepod said.
The initial premise is "what if normal people tried to be superheroes."
Then over the course of the movie:
1. In his very first attempt at superheroing our protagonist gets pummeled and run over by a car. All well and good, except for this beating leaves him with a superpower: he doesn't feel pain (and the movie seems to equate not feeling pain with not getting hurt when in the real world this
is a very serious medical condition because you still get injured you just don't know it. I'm not so much bothered by the misrepresentation of what not feeling pain means as by the fact that these are supposed to be normal people.
2. Then they make the B, bordering on A, story about two Batman level superheroes who are weapons and martial arts masters, even at 11 years old and in almost every way behave indistinguishably from superheroes.
3. Superhuman ability to continue functioning while on fire.
4. Super jetpack technology.
In the end, this isn't a movie showing "what if normal people tried to be superheroes" but rather "what if Batman and Robin had a geeky friend."
Then there's the inconsistency that Hit Girl takes out 8 guys with guns in a hallway and then 30 seconds later walks into a disabling roundhouse kick (not to mention she was going to sit there and die by bazooka without even using the grenades she had).
That said, I really enjoyed almost every moment Hit Girl and Big Daddy were on screen. I liked the set up of the "dweeb playing hero". But most of the middle was pointless and contradictory. The last act of the movie does not fit with the first. Hit Girl should have shot the GBF storyline in the face as an act of humanity.