Yes, Sauron did create the Uruk-hai, but didn't Saruman refine the process for his own purposes in the books? Anyhow, that didn't bother me as much as the fact that in the movies, common orcs and trolls pretty much go about outside in the daytime with complete impunity. As Tolkien wrote it, orcs were severely weakened and bothered by the sun, that's why he created the Uruk-hai in the first place, but this does not appear to be an issue at all in the films. In the case of the trolls, sunlight was downright lethal, hence Sauron creates the Olog-hai, but again we see trolls during the day at the Black Gates and Minas Tirith. Yes, I know some will say that it was overcast in those scenes, but PJ still made the sky look very bright, and the slightest break in the clouds would theoretically kill every troll in sight. I'm sure even Sauron could not predict the weather with complete accuracy... heck, even modern science can't do that.
On the issue of Gothmog, Tolkien, in all of his written work, only clearly ever names one of the Nazgul, and acknowledges it when he does so. This sole named Nazgul is, as you pointed out, Khamul The Easterling. Not even the Witchking's true name is ever revealed. If Gothmog were one of the Nazgul, Tolkien, who was an absolute nut for detail and placed tremendous importance on names, would not have failed to mention this very important fact in the text of ROTK. I find this omission a very telling fact in the case against Gothmog being a Nazgul. Furthermore, piecing together the sequence of events and dates of the War of the Ring as written in LOTR and Unfinished Tales, one can glean the following:
- Khamul is the leader of the Dol Guldur garrison, and among the Ringwraiths, he is second only to the WK himself. When the war begins, Sauron launches a four-pronged attack. Two of these prongs are directed at Lorien and the elven realm in Mirkwood, and Khamul leads these attacks. In UT, Tolkien writes that besides Khamul, there were two other Nazgul at Dol Guldur. One he he kept at his side, and another was used to run messages between Dol Guldur and Barad-dur.
- The WK leads the attack against Gondor from horse and fell beast, and in ROTK, Tolkien writes that five other wraiths battled in the skies against the White City. Three plus five plus one makes nine.
- After the attacks fail and the WK dies, Sauron pulls the eight surviving wraiths back to Mordor, using them one last time at the Black Gate.
I find absolutely no evidence in any text to make valid support for Gothmog being a Nazgul. I just simply can't understand how or why Tolkien would fail to mention something that important. Surely with armies as vast as those that Sauron commanded, it is only fitting that he have other commanders on the field besides the Nazgul, like the Mouth or Gothmog. I should note that in UT, Tolkien wavers between having three or two wraiths at Dol Guldur. However, even accounting for that discrepancy, he never does accord that to having any connection to Gothmog's identity, leading me to believe the two issues are completely unrelated and Gothmog remains something other than a wraith in either case.
I feel he was probably an Olog-hai rather than an ordinary orc because Tolkien's description of the intelligent trolls seems rather impressive, and there's nothing more commanding or terrifying to a large army of unruly orcs than a large brute with brains. An Olog-hai would fit the role of Gothmog perfectly, but that's just my opinion and only Tolkien will ever know for sure what Gothmog truly was.
:th