Other potential sources:
-Imperials and Khajiit. Apart from that territorial dispute/fiasco alluded to in Leyawiin in Oblivion, the Khajiit were the first ones to secede from the Cyrodiilic Empire after the Mane was overthrown by a nomadic raiding group. Imperials would probably blame the Khajiit for striking the blow that led to the shattering of the Empire, and not distinguish between those native to Elsweyr and ones actually born in the province they occupy. Most Skyrim Khajiiti most likely don't give half a crap about politics, but will hate the Imperials for what they view as persecution.
-Dunmer and Argonians, for obvious reasons. As a consequence of their long history of persecution and enslavement of the Argonians, the Dunmer were the central focus of quite a bit of anger for many Argonians to begin with. All it took was one violent-minded Hist to conduct a swift and massive invasion of Morrowind when it was cut down to its knees and incapable of mounting an organized defense. Friction on both sides, possibly hatred of native Argonians by their emigrant fellows for their disgust with the Black Marsh's sudden imperialism and hypocrisy. They keep Dunmer slaves now, over there. They view it as poetic justice, while everyone else just views it as an abomination.
-Nords and Bretons. Haven't heard too much about actual hatred in the lore, but Nords certainly don't like Bretons. They're inherently distrustful of magic, apart from the sacred Voice, and furthermore Bretons were created as a side effect of frequent cross-breeding between aldmer and humans, creating a race justifiably nicknamed "half-mer." Bretons are just not popular among them. They're also very commonly viewed as snooty or pretentious by other races. "Charming" is the best they get. They don't do manly. Nord women can do manly better than the manliest Breton. Only Orsimer women are manlier. (Then again some Orc women are manlier than even Orc men. Malacath figures you can't have too much of a good thing.)
Orcs and Redguards are on decent terms with pretty much everyone, though, so I don't see much friction with either. Orcs are often viewed as savage, stupid, ugly, filthy etc. but are well-regarded for their strength and conviction. Redguards are usually viewed as friendly and able, at worst they'd be considered crafty and untrustworthy. No specific hatreds, really, and orcs have been accepted long enough by men that it'd be unlikely to find specific hatreds of them, just a mutual cultural aversion.
Apart from interracial conflicts, conflicts within an ethnic group are also important. The Dunmer are an exiled people. I can imagine three main groups: respected elders who are old enough to remember the Tribunal's rule firsthand, who lament the loss of their home and their pride. More mild-mannered Dunmer who increasingly follow human ways, and simply want to integrate and move on with their lives, mourning the loss of their culture but discarding it nonetheless. And then a younger generation, a group of kids raised on tales of the homeland with an "I'm so Dunmer I [censored] ash" mentality. They're obsessed with their past and continue to follow the lessons of the Tribunal, worshiping them as esteemed ancestors now that their godhood is no more. They wear restored Ordinator and Great House armor, raise Netches for their leather despite the great expense of doing it in such an inhospitable climate for the animal, and frequently form vigilante groups (which sometimes end up as lynch mobs) to roam the country side and punish evildoers (or whoever seems to be a rich pushover).
Nords: Civil war, obviously.
Imperials: Hawks vs. Doves. Retake the seceded lands and restore order, or work on problems at home? Do your part. Get in a fistfight over it at the pub.
Altmer: Xenophobic vs. Integrationist. Some see the centuries-long embargo as detrimental to their people, others simply hate foreigners enough to not care.
Argonians: Those triumphant over the invasion of Morrowind, and some who dislike their empire for the crimes committed against the Dunmer. Those who left the Marsh do not hear the Hist, though. They couldn't possibly understand. The Argonians did mount the best defense against the Oblivion gates, after all. Maybe the Hist think this is the best way to protect their neighbors, and why not indulge their children in a bit of cruel ego-stroking in the process?
Khajiit: Same deal. Many would be upset over the coup.
Bosmer: Don't see any.
Bretons: Perhaps divisions along the Synod/College of Whispers?
Redguards: Don't see any.
Orcs: Again, not much potential.
So what are your thoughts?