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 middle of the film when David Banner transforms himself at the lab's gamma machine, he attacks a black cop. Watch closely, just after David Banner lifts the floor up sending the cop flying towards him you can see he is lying on his back in one shot then lying on his side in the following shot. (Slow-mo is required). (01:15:55)
Continuity mistake: In the beginning when Bruce and Betty are talking, her fringe changes several times during the scene. (00:12:30)
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: During Bruce's conversation with David near the end, he wears light blue pants, but when he transforms into Hulk until the end of the fight with David, he wears the same purple pants that he wear during the desert battle. (01:58:43 - 02:08:04)
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 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.
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).
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.