Independent research after grad school while holding a somehow unrelated career. What are the potential caveats or problems?
The main issue I can think is time. Other people who will be working on the same research field will spend their full working week on the topic while you will be working only in your free time (weekends etc.).
So you will be progressing very slowly and there is a high chance that you might get scooped if you are working on some hot research topic.
All that assuming that you have some average productivity aptitude and you are not some productivity beast that is able to finish up work in 1/10th of time than the rest :)