I have obtained business visas on arrival at Baku twice in the last couple of years. The key thing is to make sure that you have the original of the letter of invitation and also have the visa fee in cash.
The whole process took about 45 minutes, if it remember rightly. It is important to get out the plane as quickly as possible to get to the front of the queue.
Also, make sure you have a pen. If I remember correctly, the forms were slightly different from the ones you fill in if applying by post, so (and again, my memory may be playing tricks) I don’t think you can save time by bringing one of those pre-completed.
Both times I was working for one of the Ministries, so that may have ensured that my invitation was kosher (it was signed by the Minister), but having said that I didn’t see anyone else around me having apparent problems with their paperwork.
I hope this helps.
On the subject of hotels in Baku (if this info is any use to you). They are extremely expensive. I’ve used the Radisson SAS Plaza, which is all-suite, gloomy and over-heated, and the Hyatt Regency, which was superb.
Good luck and safe travels. Simon