Why does Gogeta SSJ4 have red hair?
There isn't a definite answer for this and considering the fact that Dragon Ball GT isn't canon, we aren't going to get any definite reason as to why this is the case. I wouldn't call it a mistake as certain mistakes like Vegeta's brown hair were actually acknowledged and corrected while Gogeta's red hair is continued even in the recent Dragon Ball Games like Xenoverse 2.There are a lot of interesting theories in the Dragon Ball Community. The two most common theories would be, Some people believe SSJ4 Goku and SSJ4 Vegeta fused attained a transformed even beyond SSJ4 just like Gotenks was able to attain SSJ3 in Z. While this theory is a little hard to believe, the other recurring theory which even I personally believe makes more sense is that SSJ4 Gogeta's looks a lot like SSJ4 Goku(apart from the color change) and the red color hair was done on purpose to further distinguish the 2 characters.