There are debates among scholars, and then there are scholarly debates. In pulp studies - I'm thinking of Lovecraft and Robert E. Howard studies in particular - there are a couple of points where the opinion is divided enough and the evidence sparse enough that you can have some real discussion on it.

What Was The Nature of Lovecraft's Illness? - I won't bore you with the details, but Lovecraft was self-described as a sickly kid, who suffered nervous breakdowns or near-breakdowns as a teenager which prevented him from completing school, and suffered during adulthood from ingrown hairs, an extreme sensitivity to cold, and a few other symptoms prior to his eventual fatal malady (kidney disease and stomach cancer). However, the issue is made more difficult by Lovecraft's general robust physical health, and a medical exam that found nothing wrong with him when he applied to enlist in the Rhode Island National Guard in 1917. Some folks have started trying to argue HPL was on the Autism spectrum, others have suggested vitamin deficiency, a few folks are still suggesting congenital syphilis...there's not enough evidence to really say definitively one way or another (although personally I find diagnoses of mental illness inapplicable posthumously, and there is medical evidence against HPL having syphilis).

Did Robert E. Howard Get Laid? - This is one of those things where there evidence is suggestive but not definitive; if you go through his references to prostitutes in Mexican border towns in his letters, it certainly argues he was in the right place at the right time...and then you look at some of the erotic poetry he wrote after he got back from Mexico...but he never says anything definitively. This isn't so much a debate as it is an ongoing line of inquiry because of certain ramifications it may have had if REH had sex with certain other people in his life...but I'm not sure if those have been published yet, and they're very speculative, so I'll leave it at that.

And of course, the perennial favorite...

What's In The Public Domain? - Always an issue for pulp studies, everything from 1924 and before is now in the public domain for absolute certain, but the situation is pretty muddy for later works, thanks to the complexities of American copyright law and the way pulps tended to buy rights to stories, so it's not always clear if certain materials were renewed at the right time and, if so, who now owns the rights. This is one of those things where scholarly debate slides over into legal debate, since there's usually money or publishing interests tied up in the big-name writers, but there's a lot of interest in stuff like letter's columns and unattributed essays.