Do be scrupulous about checking detail – that names of characters are consistent, sequences of events work, etc. All authors make slips, and it is an editor’s job to spot these and point them out: but if I find too many mistakes during a first reading, I shall simply abandon the book before I’ve reached the end. By the same token, if you are writing a police procedural or a book that depends on specialist forensic or scientific knowledge, do research this carefully and get it right. If you don’t, I may very well pick up on it, as editors get a feel for vague and inaccurate work; but if I don’t and the book is published, it will be your reputation, and probably your writing career, that is on the line, not mine.
Always, always, aim to get the details right... You WILL make mistakes, of course. Just admit them, and move on. :-)