What would make you guys drop a story at the first chapter?
I know you said to omit grammar mistakes, but I feel it's still worth mentioning that awkward sentence structure sometimes makes me drop a book as soon as chapter one. If it is difficult for me to the point of
needing to reread entire sentences or paragraphs with any considerable frequency, I simply find whatever hook the book presents to not be worth the trouble!
That said, an utterly unbelievable or irrelevant plot will make me drop a book as well. If I find that I cannot believe in the authenticity of the genre, plot or its pieces then I simply wont enjoy a book.
The final reason that I will drop a book, though this almost never happens in the first installment to a series, is if the series has simply--in that book--lost its charm, especially with no promise of regaining its charm. This happened with a book about a dungeon core which I read some time ago wherein, five books in, literally everybody was being revived as immortal dungeon cores with no real address to the consequences of such actions. It's also happened with regards to a number of fictitious romances I've encountered.
What would make you guys want to keep reading?
Oh, you know, stuff. Concluding chapter one, I have usually decided whether I will read the book to completion or not. There are some outliers, of course, but the majority of them are so. In reading the first chapter I should know whether or not the author writes with conviction, whether the characters and plot are authentic, whether its aspects held the author's attentions as he wrote it.
By about 75 pages in is when I will have fallen in love with a book or not. This tends to be a result of written ingenuity, be it plot, imagery or what have you. Love can be found 75 pages deep. And, love can be lost barely a page later.