Continuity mistake: When Bruce first arrives at the lab in the beginning of the movie, Betty tells them that they have to present to the review board on Tuesday. After the experiment where the frog explodes Bruce asks Betty what should they present for Monday.
Continuity mistake: When the dad of the hulk comes to see his son for the "deal" he made to turn himself in to the military. You can see the type of handcuff the dads wearing changes kind two or three times in the scene.
Continuity mistake: When Betty is talking to Bruce about accepting their breakup, the camera from the front shows her looking right at him, but the camera from the back shows her looking down.
Continuity mistake: Betty is touching the door panel to scan her identification but in the next shot she has not reached the door yet.
Continuity mistake: In the scene where Nick Nolte is in Bruce's lab, after he exposes himself to gamma rays his hair is almost completely black, but in the rest of the movie it is greyish-brown.
Continuity mistake: In the pic with Betty there is no sun on it, but in the flashback the sun is shining on the tree.
Continuity mistake: When Bruce Banner is submerged in the holding tank at the desert lab, he has hair on his chest. But when he changed back from the Hulk at Betty's cabin, his chest was smooth.
Continuity mistake: When Betty takes Bruce back to his childhood home, she sits on a swing prior to entering the house. The swing is moving as the go into the building but is stationery a few moments later (it wouldn't have had time to come to a complete standstill).
Continuity mistake: When Betty walks down the stairs to calm the Hulk down the camera angle from the front shows her hair blowing in the wind, but the camera angle from the back doesn't.
Answer: There are varying interpretations of Bruce's memory in the comics. The most common one is that Bruce has vague memories of what happens while he is the Hulk (i.e. fear, hunger, images), but because the Hulk's brain is less "evolved" he can't remember specific information, like where he went or what he did. The converse is also true: The Hulk has vague memories of Bruce's life as well...he recognizes people that Bruce knows but doesn't know anything about them.