Continuity mistake: While Dr. Morrow is saying, "I did some preliminary tests on David. The limbic system is definitely affected," he is holding a folder containing patient information and a picture. In the next shot the folder contains a different picture with no time to have turned any pages.
Continuity mistake: When David is on the hospital bed before his first transformation, he is wearing beige pants. During his transformation he is wearing light blue pants, but when fully transformed into the Hulk he is wearing beige pants again.
Chosen answer: Bruce has always been the character's middle name. In the comics he is Robert Bruce Banner, here he is David Bruce Banner. Apparently the executives behind the show preferred the name David.