getting to level 60 in palace of the dead isn't bad so long as once you're there you take the time to study your tooltips and practice your moves on a striking dummy before continuing on to real content.

The good news is right now all the jobs got a bit of an overhaul, so many people even at level 60 already went into the expansion without a full knowledge of how to play their jobs. They've had time to catch up, but if you're going into the level 61 dungeon on a job you leveled in Palace, it's likely you're not that far behind people who might be running it for the first time provided you study up before that.

Also a good leveling method not mentioned are the Vath and Vanu beast tribe quests. They scale with your level, and will continue to be a decent source of experience even past level 60 along with hunts from the Stormblood areas.