Growing grass in Alaska, man that's a short season, but with plenty of light. Anyway, what product did you use? Most, if not all, "Weed N Feed" products are a waste of money. You have to apply them to your lawn when it's wet and the weeds are actively growing. That way the weed killer will be absorbed by the plant. It's a bad method of action. A better product is a preemergent herbicide. This is applied before weed seeds germinate in the spring, and it prevents them from growing into adult plants (dandelions won't be stopped unless it is a dandelion seed). For weeds in your lawn, spot treating with something like Weed B Gone Max is a good way to go. The amount of herbicide you use is very small, and it is directed right on the weed.

Based on about a hundred comments just like yours over the past many years, we are all in agreement that weed and feed products don't work.

Similarly over the years we have whittled lawn care down to the three cultural elements of watering, mowing, and feeding. Here is the basic gist of the wisdom of the Internet lawn forums:

2. Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. If your grass looks dry before the month/week is up, water longer next time. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.

3. Mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. Bermuda, centipede, and bent grasses are the most dense when mowed at the lowest setting on your mower. Dense grass shades out weeds and uses less water when tall. Dense grass feeds the deep roots you're developing in 1 above.

4. Fertilize regularly. I fertilize 4 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above.
   

While Weed and Feed products aren't great, you made errors in using the product. You specified that you used a post-emergent product (the weed and feed) BEFORE the weeds were up - in other words, as a pre-emergent. That doesn't work. Also, most pre-emergent products for lawns work on grassy weeds, not broadleaf weeds. It's important to read what the product does, and not buy it for what you WISH it to do.

Ditto dchall and tiemco. Very good and accurate comments. Like they said, a healthy stand of turf, and a touch of pre-emergent go a really, really long way.