N+P mortgage ok on phone - worried later will be refused?? long story

Hi,
just wanted some advise on what to expect. I've just done a long application for a mortgage with Norwich and Peterborough (1year fix, 2 year tracker), which I think is an excellent deal for us.
I have perfect credit score, but my husband has 2 marks on his, both from mistakes by HSBC which they admit to and are rectifying on the experian report, but they have said that it might take a couple of months for these charges to show because they only refresh the reports every 3 months (is this true?).
The joint application seems to be ok and the guy on the phone said the credit sweep came back green, which is great. However, is there a chance the underwriters will do a later search and turn us down?? although we only want to borrow about 87% LTV, we are borrowing at the top of our 'affordability' (having to put it at 40 years, but we can overpay, so in reality it won't be).
I'm just worried we'll get so far and get turned down and then I'l have to admit when they ask during another application that we have been turned down for a mortgage in the last 5 years...if that makes sense. I know we can do it all in my name, as the affordability is fine, but perhaps them later turning me down will affect my credit score.
the bottom line is: how likely are they to do this? is there anything I can do to improve our chances?
thanks!