Deliberate mistake: In the Director's Cut (the version most readily available on DVD), there is literally an entire 15-second chunk of the final fight that is repeated twice within 60 seconds. (It's the bit where Duncan and Kell are fighting on the ground, Duncan kicks Kell, then Kell kicks and slices Duncan) It's impossible not to notice, and it's not they're flashing back to what just happened... they just repeat the same 15 seconds of footage, add different sound effects, and assume people won't notice.
Continuity mistake: After Joe shoots and kills Hale, it cuts to a wideshot of Duncan and Kell on a catwalk squaring up against each other. Duncan makes a very specific move, where he glides his sword from his right side to his left. The shot then cuts to a medium shot... and Duncan's sword is suddenly on his right side again, and he makes the exact same move a second time.
Audio problem: Right as Duncan leaps into the "chain room" in the final fight, he lets out a light "Ugh!" sound. Then, about 5-10 seconds later, when Duncan surprises Kell and kicks him... Kell makes the EXACT same "Ugh!" sound effect.
Continuity mistake: During the flashback to 1712, Connor and Duncan fight it out with highwaymen who are collecting fake tolls from travelers. Throughout this scene, Duncan McLeod's five-o-clock shadow starts out dark, becoming lighter, then darker, and then almost clean-shaven from shot-to-shot as the fight progresses. This continuity problem persists, to a lesser extent, throughout the film.
Answer: It's hard to say. Since the series totally ignores "Highlander 2" some assume that they also ignored "Highlander 3." But if you don't like that idea, you can probably assume he's off at college with his own life, or maybe even been killed by Jacob Kell.