Did you see my posting about multiple mushrooms?
Here are some other tips, etc. I've come up with:
1) When training a "healer" I'll sometimes put him/her on another of the special plants. The villagers can still learn about healing there (I don't know if there is any speed difference) but since there aren't always kids or other "curious" villagers around it makes it easier to keep track of the "medical school."
2) When training a builder and there is a hut on the "west side" of the village that is being built, I'll sometimes wtach whether the builder is going for a rock or some wood. If it is the rock, I'll "start that class again" until he/she goes for a wood. The reason is that that skill isn't learned until (maybe) after adding the material to the new hut, and the time spent to the material and back is shorter for the wood.

BTW, when the builders are fixing the huts, I've never seen their skills improve when the hut is in good repair.
3) It is quicker to train a farmer via foraging than fishing or harvesting/planting/watering.
4) I didn't discover this, but I'll add to my "training class." When training the scientists, watch for that little "side-step." That is when the tech points are earned, as well as adding to their skills.
5) And to complete the set: Parenting skills are only earned by the parent who initiates the "kiss." As other have said, if the population doesn't increase immediately, just pick up one and try again, even if they are on the way to the "love shack." A Villager will there preferred job set as "parenting" will always try to "romance" the first villager on the details list of the appropriate gender (as long as he/she isn't sick or already nursing.)
I'll post more later...