Why do agents request only a few pages to look at rather than the whole manuscript right off the bat if your query is amazing? Because we can tell what your writing style is like within the first few pages.
What if you want us to look at pages further in the book because they are better and the first few pages aren't representative of your work? Then revise your first section.
I've seen plenty of manuscripts that pick up after fifty pages, but that's fifty pages of work we have to put in (for free, and we have to weigh if the gamble is worth it). There is plenty of advice out there on first sentences, first pages, and first chapters. If you read my Wednesday Reads, you'll see how much weight I give to a first line--the ones I really love is when I don't want to stop at the first line, but give you several, or whole pages.
YA Highway recently did a blog post on the importance of using beta readers, which yes, I'll agree is very important. But even if you have a professional copy editor edit your work line for line and every sentence is grammatically correct, it doesn't necessarily make for a book deal. Ever read a textbook front to back without falling asleep? Grammatically correct? You bet. Boring as heck? You bet. Why? Story. Plot. Not delving into the anatomy of a whale for fifty pages... Am I talking about Moby Dick now too? You bet. Melville's sentences are grammatically correct as well, but I would never suggest a writer in today's market write a half page long sentence using fifteen semi colons (please don't).
For me, one of the quickest ways to test a writer's skills is to read a section with dialogue. It needs to flow well, read like a real conversation, include enough description to lend action, have voice for each character, have it's own dialogue arch, emotion, and have a point. You can't have a conversation for the sake of having a conversation. I also look to see where the first conversation comes in. If it's ten pages in, I start to worry about back story dump. Sometimes there will be long breaks without conversation in which the writer tries to move the story forward by summarizing--sometimes it works, and sometimes it doesn't.
So, your friends and computer spell check are probably great resources to go to for grammar and spelling, but beware of people saying "It's good." Ask for constructive criticism. Beg for it. Even published books get scrutinized--or we wouldn't have book bloggers--and the reviews never stop at "it's good." A good critique group is invaluable. Having a professional look at it is even better (editors, work shops, industry friends), because they will tell you specifically what works and what doesn't and (hopefully) never leave off at "it's good."
Summing up, use your beta readers, but don't put all your stock in them. Use critique groups, workshops, and professional editors (who don't stop at grammar but look at content and pacing). If your ms is getting rejected after a few pages, you're sure your query is good (you'll know by how many agents request to see samples off your query), and your plot is unique, look at the writing. It might not be up to par yet. You might have errors in your ms that have nothing to do with grammar that still scream "Newbie! Newbie! Newbie!"