I've noticed on many occasions that my edits-per-paragraph are generally much higher in the opening two or three paragraphs of a story than anywhere else. I occasionally wonder whether that's because I get drawn into a story and stop paying as close attention to the words and punctuation and such, but I don't think that's true; I'm certainly capable of giving a lot of edits on later paragraphs, it just doesn't happen as often.
Partly it's that I generally want to help ease the reader into a story (unless it's the kind of story that's meant to slam the reader into a new world without any help and let them sink or swim). At the beginning of the story, the reader may have no idea what kind of story it is (though reading the pull quote may give them a hint). Helping them get oriented, by providing little signposts, can do a lot to draw them into a story. If the opening paragraph is filled with complicated sentences that require a lot of work to read, or with lots of alien words that readers won't be familiar with, or anything else that pushes the reader away rather than welcoming them in, I may suggest filing off those rough edges.
Before y'all jump on me, let me reiterate that there's definitely a place for rough edges. I don't want to make things too easy for readers; I feel that readers should (in most stories) have to do some of the work of making the story work. But I'm very aware (perhaps to the point of oversensitivity) of how easy it is for a reader to get confused, bored, or otherwise turned off by a story and stop reading it. And I think the stories we publish are compelling enough to keep that from happening for most readers (of the sort who find our stuff interesting) once they get into the story, but my theory is that it's easier to give up during the first couple paragraphs than later.
(Also, my edits are almost always just suggestions; if the author disagrees, that's their prerogative. Author gets final say.)
There are other factors, too. For whatever reason, there seem to me to often be more tense problems and confusing phrases in opening paragraphs than later in stories. And that's where an author establishes the stylistic conventions they'll be using, so if I have queries about such a convention ("Do you want thoughts in this story to be italicized?"), they'll often appear in notes on the first couple paragraphs. And those paragraphs are also often where a setting is established, and sometimes settings need clarification.
But of course, it could just be that as I keep reading, I get drawn into the story more myself and get less nitpicky.