Independence Day (1996)
. Miguel refers to Russell by his first name for most of the movie. A deleted scene reveals that this is because, as Miguel tells Russell, "You're not my father. You're just the guy that married my mother." This also explains why Miguel looks very little like Russell.
. When David is driving to Washington DC to alert Constance, he tells his father, "She always keeps her cell phone listed for emergencies." When he calls her, she answers the phone and says, "David! How did you get this number?" A deleted scene explains how he tracked her secret cell phone number down by searching for various aliases she's used in the past - in this case, it was her married name.
. When Jasmine is first seen dancing, it soon cuts to her saying, "I came to get my check and I got talked into working." If one wonders where her son is while she's working unexpectedly (no time to call a sitter), a deleted scene shows him and Boomer the dog in the manager's office waiting for her. This is part of the reason she quits - her boss yells at her for "bringing that kid in here."