I'm thinking about buying Duke3d, but I remember that a week or so ago several people were complaining about not being able to order games. Has the problem been fixed?

You just missed a promo on it. Oh well.
I bought King's Bounty and UFO Afterlight in the last promo without issue. But that was with Paypal. The problems have always been with credit cards. In fact I'd recommend using Paypal with all DD sites as credit cards often seem to cause problems.

GOG was having an issue and when it was resolved they extended the Promo. I was able to get the Promo without issue after the fix.

I tried to buy a game and had a problem using credit card. I contacted my bank but haven't gotten a response yet. Is the problem on GOG's side?

I bought King's Bounty when it was on sale last week using my credit card and I didn't have any problem.

You can just try it. If it doesn't work, bitch and moan, if it does, you own Duke Nukem!