Does the DNA or RNA of some ethnic groups map better than others' to the human reference genome sequence? I believe that the human genome reference took DNA samples from different people and that some natural variation is included in extra contigs. 

However, the human reference genome comes from a limited number of people. 

Can the limited number of donors and the linear representation of the genome (as opposed to a graph representation that could potentially include variation) bias an analysis in favour of one ethnic group over another? Are there studies that have compared the alignment rates/mappabilities of reads of people coming from different geographic regions? Do some ethnic groups' reads align better to the reference?
For simple variants like SNPs it would not really be a problem to use the current genome assembly for other ethnic groups. But for more complex variants this could be indeed problematic, however not only for ethnic groups but also for individuals within the same population. Think of very complex regions such as HLA or KIR.

In studies where they compare different ethnic groups (e.g., 1000 G) they rather not discuss such matters, but act like the analysis is 100% perfect.

There is a nice comment in Genome Biology about this issue.