I also had this problem for a while and was unable to progress in any of my quests. I finally got it to work after trying the dig spots in a different order as people have been suggesting. After completing the part of one quest that required dig spots on different islands, I turned it in and tried a different quest that required dig spots, which still did not work. Luckily, I found that the dig spots for another quest had started working, and after completing that quest the other set of dig spots worked too.
The glitch had started once I got the quest for the dig spots on multiple islands ("Family Valuables").
Thank you for that information. I will check when I get home if I have other dig quest and try them first and in different orders. Any hope to get my daggers will be great.
I hope this bug gets fixed soon.