Partial Grigori genes seem to manifest primarily through three characteristics: exaggerated physical proportions, unusual coloration or patterns of the skin, and shifts in mental perception or character. All pureblood Ellehemaei have some degree of personality shift, but those are less significant than what I mean here. Most positively, Grigori genetics can (and frequently seem to) impart enhanced mental abilities. However, it can also have such severe effects as psychosis, split or entirely rewritten personalities.
On my previous note of more aquatic, fish-like characteristics, I would like to revise that particular hypothesis. I do still believe that the Grigori genetics lend themselves more towards water or aquatic elements than the other two bloodlines. However, I now believe it to be, more specifically, the effect of Grigori genes on Daeva genes.
This parallels my prior tentative hypothesis of more plant-like Changes being a combination of Grigori and Mara genes, but you may notice the difference in phrasing. That is intentional and related to my revised conclusion: Grigori physical characteristics are all inherently humanoid, but they can strongly affect the expression of genes from the other two bloodlines.
This is especially interesting when taken with the fact of the pureblood personality shifts. If one takes the premise that Grigori genes primarily function to strongly influence the expression of the other bloodlines' genes, a primarily Mara halfbreed could feasibly evidence a more extreme but still Mara-like personality effect. (I suspect this is evidenced in one particular case, where a clearly Mara-dominant halfbreed can, after Changing, no longer experience fear. This is a very Mara-like characteristic, but not a very Mara-like Change.)
Stronger Grigori influence would obviously have more of an effect of their own right than simply altering or enhancing elements of the other bloodlines, such as the aforementioned proportions and coloration.
Additionally, while I continue to hold to my "elemental" associations from previously, I also now speculate that being what one would view as "an elemental" - having a Change which makes you largely "into" that element, with some significant degree of control over it - is a sign of strongly Grigori genes.
And lastly, I would like to rescind my prior hypothesis of Mara genetics expressing a tail. I believe that is a solely Daeva characteristic, and that the presence of a tail on Changing is a good indicator of some Daeva ancestry (although not necessarily of a strong influence).