Possibly. Depends on why the neighbor was filming, under what circumstances, and among other things whether the DA could get the tape authenticated and introduced as evidence....its certainly possible.
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Yes, possibly. You might have some defenses, depending on who was doing the filming and how it was done. It might also depend on what you were doing. For example, if a person is involved in or suspected of terrorism, the government can/will/does justify violating that person's constitutional rights.
If you are doing something illegal, make sure you keep your curtains closed.