Finalizing a patent application should be the job of a corporate attorney, or at least an attorney who specializes in patents. One would expect Palmer Industries to have an attorney or two on staff and not rely on Felicity to do their legal work.
Laurel should have recused herself from any involvement in Oliver's case, including and especially deciding not to prosecute him, based on her years-long personal relationship with him.
After Captain Lance is done talking to Roy in his jail cell the guard unlocks the cell door to let him out. A buzzer sound can be heard as he turn the key to the door. The cell door is a manual lock and does not make that sound. The sound used is from an electric door lock buzzer.