Rampant problems that should have been caught during editing is the number one complaint I hear from self-publishing's detractors as to why self-published books aren't worth reading. When a reader picks up a book and finds multiple, obvious grammar and sentence structure mistakes on page 1, chances are they'll put the book down and not pick it up again. Chances also are they may not give you, as the author, a second chance.
I'm not saying professionally edited books won't and don't contain mistakes or oversights. I see them all the time in traditionally published books, which I know go though professional editing. I read one not long ago from a big-name traditional publisher, in fact, that had so many mistakes in one paragraph that I had a hard time figuring out what was actually being said and what the author intended to say, and there were a handful more on that same page. Only thing I could figure, since most of the rest of the book was fine, is the editor missed that section of the book during edits. (Either that, or their typesetter was REALLY not paying attention at that point.) There were two places like that in the book. Considering the book was almost 300 pages long, that's not bad enough to make me toss the book altogether.
As an author friend of mine noted, it doesn't matter how many eyes you have look at a book, something will probably slip through. So don't expect perfection, no matter how good the edit job is.
That said, hire an editor, or at the very least find a good critique partner who will be honest with you about issues they find, however few or plentiful. Editors are paid to be brutally honest and usually are. (And not all editors are created equal, so make sure you find a good one.) Critique partners may feel the need to spare your feelings. Let them know you don't WANT your feelings spared. You want the truth so you can polish that MS and make it as professional as possible.
A few mistakes or oversights is way different than rampant issues that a second set of eyes on the MS would have caught. I'm the type of reader who will generally power through such problems, no matter how bad they may be, to look at the story and characters. Other readers won't necessarily be so determined, or forgiving. My internal editor may have screaming fits, and I have to restrain my desire to go to town with a green pen (Thank you, Mr. Sullivan, for THAT particular habit *G*). But I'll get through it to see what the meat of the story is.
And take it from me, no matter how many times YOU look over your own work, you're going to miss stuff. I've learned this the hard way. I've been amazed at what obvious stuff my critique partners and editors have caught that I missed, no matter how many times I went over that MS.
So find a good editor or brutally honest critique partner and edit your work! Your readers will love you for it.
Next week, that second issue I often see....