I get the impression that taxonomists generally accept two taxa, P. glanduliferum/praestans and P. wilhelminiae.
One question is whether or not glanduliferum = praestans (e.g. Cribb 1998) or glanduliferum is a 'lost' species and praestans is the currently grown species (e.g. Braem 2003). I tend to agree with the glanduliferum and praestans are different opinion. Although, I have seen a pic of a wild-collected praestans with a pale-but-still-striped dorsal sepal that might indicate they are conspecific and just at two ends of the spectrum of variation within the species.
As to P. bodegomii, status is easy. It was never formally described and no type specimen has been found so it can be regarded as a trade name only.
P. gardineri was published n 1886 with the type being a poor line drawing. It lacks enough detail to even begin to distinguish between the species, so most authors consider it invalid. Garay (1995) in using staminodes to distinguish between the species, does consider P. gardineri to be valid. I have never heard anyone remark favorably about Garay's analysis. In the trade, it seems that most of the time that I see P. gardineri offered, it is P. wilhelminiae that is really being sold.
P. praestans can be separated from P. wilhelminiae based on: (i) flower count, P. praestans generally 2-4, P. wilhelminiae 1-3; (ii) flower size, P. praestans significantly larger; (iii) bloom background color, P. praestans pale yellow background, P. wilhelminiae ivory to white background; (iv) petal color, P. praestans pale with indistinct chocolate striping, P. wilhelminiae very darkly chocolate-striped, stripes sometimes merge to form almost solid-colored petals; (v) petal twisting, P. praestans petals helically twisted 3-4+ times, P. wilhelminiae petals helically twisted 0-2 times; and (v) plant size, P. praestans significantly larger, I have heard of a first-bloom P. wilhelminiae with a 6" leaf span.
There is also a significant geographical difference between the habitats of the two species. P. praestans is found in northwest New Guinea and its adjacent islands, whereas P. wilhelminiae is found in the mountain chains of central New Guinea. (
http://www.slipperorchids.info/paphdatasheets/mappoly.jpg)
I have also heard of the presence and number of warts near the base of the petals being used to distinguish P. praestans and P. wilhelminiae, but I haven't noticed a significant enough difference in my limited experience to find them diagnostically useful. I don't know anything about the differences in the raising of the stripes on the sepals, as I have never looked for it when looking at blooms. I will have to remember to do so the next time I see a member of this complex.
I think this is one of the Paph species complexes that is most desperately in need of field studies. I don't think anything can be said for certain about this complex until more extensive work has been done in situ examining the natural variation of the species.
I was in Capon Springs, WV at a tiny resort for an annual family reunion. A week of golf and sitting around. It's a rough life, but someone's gotta do it...
--Stephen
p.s. Garay's 1995 analysis that appeared in OD is available online:
http://www.orchidspng.com/contrib_garay2.html
Mine don't seem to bloom for me, even on 4 or 5 growths. Not sure what I need to do. 
