Dangling modifiers -- you hear about these most often in jokes about what a copy editor does. "Oh, do you get a lot of satisfaction out of fixing comma splices and dangling modifiers?" (chortle, chortle)
Why, yes, I do, thank you very much.
I think the people who make these comments don't even know exactly what these sins are. (And they are sins, don't kid yourself.) Or they know what they are, but they don't think they're important.
Fools. (See, I can say that because if you're reading this, you obviously care and therefore are not a fool.)
A modifier is dangling if the subject it's modifying is missing, or just implied:
Having eaten dinner, the TV was turned on.
The modifier here is "having eaten dinner" and it's supposed to be modifying the person who has eaten dinner but, because of the passive voice (another severe offense), there is no explicit subject (person) named, so the modifier is left dangling -- or worse, it's modifying TV, which produces this meaning: The TV ate dinner and then was turned on. Hmmm ...
I think it's clear that the sentence should be recast to: Having eaten dinner, the person [or well-trained cat] turned on the TV.
A similar offense is the misplaced modifier: Flying around the room, I saw two moths.
Here, we have an explicit subject, "I," but it's misplaced, making the sentence actually say that the speaker is the one who was flying around the room, not the moths. So I guess this might be the case if Superman is the speaker, but otherwise, you would need to fix it by simply saying: I saw two moths flying around the room.