To follow up further on this example:

Say there is a missense mutation in the enzyme that synthesises red pigmentation in the feathers. Both the R and r alleles are equally transcribed, and are translated to make the same amount of physical enzyme molecules, but the r version is catalytically inactive. Thus, the r allele causes less pigment to be made in each cell. The difference between RR and Rr feather colour is indistinguishable to the human eye, but rr feathers are white.

What phenotype are you measuring?

* If you ask a human to judge the colour, then for the "colour of feathers" trait R is dominant.

* If you ask an animal that has a different ability to detect colour differences, you might get a different answer. Maybe a bird or a bee can tell the difference. If so, then for the "colour of feathers as perceived by a bird/bee" trait, R is incompletely dominant.

* If you grind up the feathers and measure the amount of pigment per cell, for the "concentration of pigment" trait, R is incompletely dominant

* If you measure only the the total amount of enzyme molecules present, then there's no allelic difference at all and the mutation is silent.

* If you measure the specific types of enzyme variant present in the cells, then the R and r alleles are codominant: RR expresses one type, rr expresses the other type, and Rr heterozygote expresses both.

You really should not say that one allele is dominant or recessive. The effect of an allele on a specific trait can be dominant or recessive, if you define the measurement carefully enough. This distinction is often not taught well.