Try completing Search Gorga objective. It is an easy one anyway and now that I rethink it must be one of those that are required since it affects how NAPA treats you in following missions. It is also one of those that are mentioned in mission Briefing->Notes->Mission section when objective names have not been revealed yet. So it may be one of the first and/or important ones that were designed for this mission.
Report Cpt. Shaftoe objective can be completed in the start when you exit aircraft, but there is a time limit, so if you do not go there early enough that objective will be marked as cancelled. In the end same objective is available again with the exact same name. So yes it should pop up again if you completed it once in the start.