Hi Nick,
I love the Fiskars weed remover too!
If you have lots of dandelions it is a sign that your soil is not supporting your lawn. The most common problem causing tons of dandelions is compaction. So I would aerate your lawn and overseed with a grass seed well suited to your climate. I would also have the soil tested. you may need to balance the pH with some lyme or replace missing nutrients. Soil bacteria don't just need N, P, K, so
compost is a wonderful way to replace nutrients in a balanced manner.
And Miles makes a good point, part of it is a change of outlook. Healthy children playing on a lawn with a few dandelions is much better than using toxic stuff to get rid of them. I have dandelion recipes in my book by a good friend and a well known cook book author Ed Giobbi.
A lot of people are changing the way they look at dandelions. Our garden club visited Martha Stewart's farm and there were dandelions and buttercups in the fields because she thinks they are pretty.