"I have been an avid reader of your blog and books for a long time and wonder if you have a short burst of blog advice for people like me who need an expert in a technical field to cast an eye over a fiction manuscript to ensure that I am not committing any factual sin.
If you can isolate the sections that require verification and there aren't too many of them, you might find that it wont' take too much of their time. If they have to read the entire manuscript and there are lots of things to check, then probably they'd find that too demanding.
I'd just add to this for other readers, don't be afraid to approach an expert for help. In my experience, most of them are flattered to be asked and as long as you are respectful of their time they will be delighted to help you.