I have a problem. Being the rank amateur DIYer that I am... I thought I could easily apply stain using a floor buffer after watching many Youtube videos describing the process. Here is one example of an informative video describing the process:
https://www.youtube.com/watch?v=NzSOXZlgPRs

The floors I have recently attempted to stain was probably installed in the 1940s using red oak. The floors were professionally sanded and were flawless when they were sanded. I assure you that there were no gouges or marks evident when the floor was sanded. So, the swirl mark errors were completely my doing when applying the stain using a floor buffer and circular carpet pad soaked with stain.

Here is what happened... There was an initial process of learning how to control the floor buffer machine. It took me maybe about 20-30min to really get the hang of controlling the machine. The problem is that the first 20-30min that I took learning to control the machine was done while applying stain to my floors. That area that was stained during this first 20-30min is precisely the area that I now see these staining swirl marks. What I think happened is that I did not spread out very evenly the stain on these areas, and hence the stain dried in this swirl mark type of pattern. Later when I figured out how to control the machine better was I able to even out the spread of the stain out more evenly.

My question is, what can I do to now fix the staining swirl mark areas? Would I need to apply another coat of stain? Or would I have to start over and sand everything down again?