Having seen a lot of recommendations, we applied for these a few weeks ago (DH is over 65, I'm not so he took single 1 year and 3 year bonds at the maximum holding for each.
It seemed to make good sense as the money was in a 'building society and interest rates are so low - as you say, our savings are no longer replenished with any interest that can be referred to as anything but pitiful and are dwindling - exactly! I've not seen anything about problems - the things I've seen come down in favour of it being a sensible investment.
We applied for the first one by post, DH having lost his NS&I password (sigh) which had to be sent by post so we just printed a form off the website and posted off the application. We applied for the second bond online once the password had been resent and we had no problems.
You can check online on your NS&I account to be sure the bonds went through all right. We ticked for 'no paper confirmation' but I think they sent one anyway.
We had to transfer the money from the BS into DH's current account and wait till it was definitely there so he could use his DEBIT card to pay for the bonds online, so the process takes a little while, but no special issues.
Tax is deductible but at the maximum holding there should be a worthwhile but not astonishing windfall - a coach holiday to Margate rather than a tropical cruise 