The first thing to check is that you've had all the necessary conversations necessary to trigger the event you are trying to start.
Not all tasks will necessarily show in your to-do list. There may be an area with an unfinished conversation or mission, so check all of your previously-discovered areas. There may be an important conversation or task that was missed.
Sometimes, it is however possible to be unable to advance if you are trying to play on two devices. The game does not allow more than one device to connect to the same account at the same time. Trying to switch back and forth quickly can cause sync errors. For example: if one starts a job on device A, finishes it on device B and then goes back to device A before the two devices have time to sync, quests may appear to be unfinished even though they have been completed on the other device.  
iOS users might also consider setting their iCloud sync to "manual” so as to have better control over syncing and backup.
If you're assured that the above solutions have been exhausted, Customer Care may be able to help; create a ticket by tapping the gear icon, then "Customer Experience" to create a ticket.