finishing old quests to trigger new ones
Yes you have to finish a\the quest line at a lower level before completing a higher level. This does not apply to randomly generated tasks.
Forum Discussion
One possible exception to this is the latest two levels. I had started the Dolph quest line (level 36) during the Halloween event, but didn't finish immediately due to wanting to keep Bart and Nelson on their GOO tasks. When Level 37 came after Halloween, I was prompted to start the Kirk quest line despite being in the middle of the Dolph quest line.
