Do I effectively lose two opportunities to have an encounter when I get arrested by patrols?
Delayed means two things


The investigator cannot move during his turn
The investigator does not receive movement points during his turn


Everything else is still on. You'd get your normal encounter for the area you are in, you can trade items, etc.

Arrested is worse.
Yes, you would miss your entire next turn, including the encounter.  Thereby effectively losing two encounters.