To answer a question that's been bothering us all

for far too long, I looked up "dangling participle". I was wrong to say that they don't bother me, it's just that I hadn't seen an adult write one for so long, I'd forgotten what they were.

Noun 1. dangling participle - a participle (usually at the beginning of a sentence) apparently modifying a word other than the word intended: e.g., `flying across the country' in `flying across the country the Rockies came into view'

And, as a bonus (or in lieu of one):

dangling modifier, misplaced modifier - a word or phrase apparently modifying an unintended word because of its placement in a sentence: e.g., `when young' in `when young, circuses appeal to all of us'

So now you've got all your danglies in order.

Courtesy of The Free Dictionary.