In a thread on the Plant ID forum, @skopjecollection expressed some doubt that this plant is S. multicostatus, and may actually be S. crispatus.

The thread "What type of cacti/succulents do I have?" in Plant ID forum

I am starting this thread so the question may be resolved and the image moved if necessary. I am no kind of expert on this subject but hopefully Stefan can help guide us, and I would like to ask @mcvansoest to weigh in if possible, too. I realize the image comes from Wikipedia (and was originally taken by one Catherine Shaw, based on a reverse image search) but it would be good for us to determine the database location from the features visible in the photo.

I see 4 images for this species, all different plants, taken from other sources on the web, and would also like to ask if if the cactiphiles could take a look at the other 3 while we're at it, and double check those IDs too.

I cannot say for certain.
1. It could be one of the spinier multicostatus varieties/similar species (erectocentrus), but the general rule of thumb is multicostatus spines should have a lighter hue, ...
2. It could be crispatus or one of the many varieties(or species associated) as i suggested, but without being able to see the full plant, i cannot say for certain.
So, i would like to point out that the flowers are quite large.Without having a size reference....this adds to the confusion..for any experience of mine anyway...

For the 4th photo they give the location where it was taken - so if someone can determine the area of occurrence of this plant one should be able to confirm whether or not that ID make sense.
Based on a really rough check - this one is probably the real thing as only multicostatus is listed for Durango in the place where I checked.

The other plants all appear cultivated, which means that to compare them to the wild version can be difficult as wild growing plants are generally grown under so many more harsher conditions.

I generally find spine color a really difficult characteristic to judge as in some many species it depends on the growing conditions of the plant and how old the spines are.

Other than that the only thing I see that makes me think that the first and third pictures are probably multicostatus is that both have central spines that are oriented generally downwards and outwards and less upwards. The major central spine on the crispatus tends to be much more upward oriented. With that note in mind the second may not be, but I am not sure that the spine orientation is diagnostic in this case.

Bottom line: I guess my argument here is that if these were posted according to the label they came with and there is no overwhelming evidence that they are something else, then maybe they get left where they are. Personally looking at a number of pictures of different Stenocactus species, many either look very similar or there is a lot of mislabeling going on.

I see Stefan's point, but if I were making the decision I'd want to see some more convincing evidence. Not saying he could not be right, just saying that to me there is no overwhelming evidence.

I spent some time this afternoon looking at pictures of both species, and reading about them, and have concluded that both species have wavy ribs, and both species have a lot of them, thus the literal meaning of the Latin species names would apply to both plants.

That said, and given the extreme variability of the individual species (which Anderson calls "a taxonomic nightmare", adding "spine color and number variable" for crispatus), the two species are hard to resolve when they are young. Based on the reference by Anderson, these are the differences I would think are most useful. S. multicostatus has potentially more ribs (as many as 120, compared to 25-60) when mature. S. multicostatus has 3 central spines, whereas S. crispatus has 1-4 when mature (though young plants have fewer evident centrals). And of course the origin speaks to the species involved (multicostatus is from the northern states of Coahuila, Chihuahua, Durango; crispatus from Zacatecas in north-central Mexico south into Puebla and Oaxaca).

Based mainly on those criteria, I see no reason to move any of the 4 plants currently in the database for S. multicostatus, but I'm open to some convincing.