One important point is that redpolls molt only once each year - in late summer. So the pale tips and edges of new feathers will gradually wear off during the year, leading to a slight but significant darkening of the plumage month to month throughout the year. This is not a big issue for birders in the field, since we will generally be comparing redpolls to their companions in real time, but museum workers have to be careful to compare only specimens from similar dates. It is suggested that Troy (1985) - who concluded that there are not two distinct populations - did not adequately control for date and for age and sex.
What Seutin et al found is that specimens can be sorted by measurements, with pale (Hoary-types) having shorter bills by about 10% on average; means of 7.67 mm for dark birds and 7.01 for pale. Taking their mean for bill length +/- 2 standard deviations (I'm told this will encompass about 95% of all individuals) the bill measurements don't look so different:
Common 7 - 8.2 mm
Hoary 6.5 - 7.5 mm
In other words, the differences are very slight, and there is extensive overlap, with the largest Hoary matching the average Common and the smallest Common matching the average Hoary.
Importantly, measurements of bill depth do not differ significantly between the species, so a Hoary should have a short and stout bill (if a 7 mm bill can be called stout). In other words, a Common's bill should be longer and more slender, a Hoary's shorter and stubbier. But this is also subject to overlap, and we don't know if the longest-billed Hoaries still have a relatively thick bill or a bill shape just like Common (or if the shortest-billed Commons have slender or stout bills).
Measurements of tarsus and hallux (hind claw) were also significantly smaller on pale birds, but it is not likely that either of these measurements will be helpful to birders. Wing and tail averaged very slightly larger on Hoary-types, but not significantly so.
In their study of plumage, Seutin et al. found that most adult males could be distinguished by darkness and thickness of streaking on flanks, undertail coverts, and rump, but that females and immatures were much less distinct. They also studied forehead color and "poll" color (the red crown patch) and found no significant difference. Unfortunately they did not measure scapular color, wing markings, neck markings, or other plumage features that now seem like they might be useful.
Breast color also distinguished nearly all adult males in summer, with Commons having deeper red color and Hoaries a pale pink. This color is obscured by pale feather tips in fresh plumage in fall, which gradually wear off to reveal the reddish color by summer. Some of the underlying color is usually visible from at least December on, under the fringing whitish feather tips, and may be a helpful clue on adult males. But this should only be used on adult males with unstreaked and extensively colored breasts (see Brooks, 1973) and these birds are generally the most easily identified by overall darkness.
Brooks, W. S. 1973. A tentative key for sex determination of Common Redpolls (Acanthis flammea flammea) in the northern United States during winter. Journal of Field Ornithology 44:13-21. pdf here
Seutin, G., et al. 1992. Plumage variability in Redpolls from Churchill, Manitoba. Auk 109:771-785. pdf here
Seutin, G., et al. 1993. Morphometric Variability in Redpolls from Churchill, Manitoba. Auk 11o:832-843. pdf here
Troy, D. M. 1985. A Phenetic Analysis of the Redpolls Carduelis flammea flammea and C. hornemanni exilipes. Auk 102:82-96. pdf here