Part 2 with the hodge-podge of foreign rikishi originating from countries other than the US and Mongolia. For the most part I'm only going to mention those rikishi for whom I have something reasonably useful to add; the rest are either guys whose data looks correct or who are so obscure that I have nothing. But I'm going to add links to the DB's country overviews, so feel free to take a look yourself, maybe you've got something I don't have. Relevant umbrella reference: Wikipedia's list of non-Japanese rikishi.
  Argentina (2 rikishi) Hoshiandesu - the accent on "José" might be worth adding. Hoshitango - naturalized in October 2000 while active per ja.wiki (don't know the exact date), real name adopted as 星 誕期 HOSHI Tango.
Brazil (16) Hakusan - A 1978 newspaper article from Texas makes passing reference to him and gives the name as Pasquale BOSCHE, so reversed order from the DB and spelled a bit differently. I noticed that Wikipedia already gives that spelling. Anyone remember the source? Azumakaze - Wikipedia has opted for a different name order, as Tuzatto Giuliano KOCHINDA. No idea which one is right,  nor if the transcribed name parts are spelled correctly. Kuniazuma - I think his names are reversed (should be RAMOS as surname); in addition the Kyokai has his given name as Vander and so does the guy himself, assuming this is a real Facebook account. So, Vander RAMOS probably. Ryuko - Wikipedia has his given name(s) as "Luis Go", A 2005 article by the New York Times has him as Luiz Go IKEMORI - I'm not sure which spelling to trust, but I think the presence of a second Western given name should be reflected. Has a ja.wiki article which mentions that he was naturalized on 1996/04/22 (same day as Akebono) and has been just IKEMORI Go since then. Takaazuma - Wikipedia has "Christiano Luis" rather than "Cristiano Luiz". Can't find anything firm either way, but I do think the DB is wrong in treating "Luiz" as part of the surname; I think that's just DE SOUZA. The Kyokai no longer has his real name listed on the English side (a lot of these seem to have disappeared in the site changes of the last few years) - I assume the DB's spelling originated from there, but I'm not sure theirs was correct. In general, my impression is that the Kyokai's online katakana name transcriptions were less trustworthy before 2006 or so. Masuyama (Brazilian origin, JP shusshin) - I'm not positive, but SOUSA is probably part of the surname.
Canada (2) Kototenzan - became much more famous after sumo, of course; might be worth expanding to his full name John Anthony TENTA Jr., per Wikipedia. Homarenishiki - not sure if it was typo'ed in the DB or if the Kyokai fixed the spelling later, but I think the first name should be Brodik as given by the Kyokai now,  not "Brodick".
China (12) - I'm relying on the extensive Wiktionary hanzi data for these, and assuming pinyin style romanization. Most of these are just housekeeping fixes, confirming readings or making small spelling changes. I would really prefer if somebody who actually knows the Chinese language could re-check these! Kiyonohana - ZHANG Lihua (no space) Kaiho - PAN Yi should be correct. Takao - WANG Yu (not Wan) Kanoyama - possibly YE as the surname - the hanzi 叶 has two derivations and two readings, but the name reading appears to be YE and not XIE (neither the traditional nor the simplied form appears at the latter link). Unless there's a source that specifically confirms a variant reading for this guy? The first hanzi of the given name also has two readings, so no idea if it should be Chengyue or Shengyue (but in any case, it should not have a space). Kotoo - WANG Shidong (no space) Nakanokuni - I've always wondered, where did the Japanized(?) "Ro Cho" alternative reading come from? I don't believe he had any connection to Japan prior to coming over as an adult, did he? LU Chao should be correct. Sokokurai - We already fixed his name reading to Enkhtuvshin a while ago, but the Japanese name field still has the Kyokai's clumsy attempt of 恩和とう布新, with a replaced character due to encoding limitations. The Chinese Wikipedia says that the middle character should be 图. I think that's in Unicode, so no need to stick with the hiragana replacement. Kosei - GAO Shiqiang (no space) Chiyohakuryu - Do we have any non-Kyokai source for his name reading? "HAKU Koto" for 白 光斗 sounds like a Japanese reinterpretation to me, not like a Chinese or (Inner) Mongolian name. Actually, 白 光斗 itself doesn't look very much like a Chinese name, though I guess it's probably a character transcription of a Mongolian name (like Sokokurai's).  Anyone have insights here? Ryutei - LI Weifu (no space)
Egypt (1) Osunaarashi - I suspect what the Kyokai put in his real name field is not quite accurate, but I've seen "Sharan", "Shalan", "Shalaan", and probably even more versions since he debuted, to say nothing about the other parts of his name. Is there somebody who has some definite info? (John?) I realize that transcribing names originally in Arabic is a bit tricky.
Georgia as Gruzia and as Jōjia (4 total) The four Georgians are a good example of what a mess the Kyokai's "official" data can be - the first three were listed as Surname Givenname (both JP and EN pages), but Tochinoshin was then listed as Givenname Surname (also both JP and EN). Anyway... Gagamaru - names reversed, should be Teimuraz JUGHELI. Easily confirmed with a Google search showing Teimuraz as a very common given name and Jugheli as a reasonably common surname.
Korea (16) Kasugao - the given name was fixed by the Kyokai at some
point to read Sung Tak. Kaihakuzan - the Kyokai has BAEK Yoongi now. I suspect the whole issue of Korean name romanizations needs further attention (e.g. Kasugao's looks like it might actually have to be Seong Taek by "proper" romanization), but that's way out of my depth, so I've only mentioned where the Kyokai has seemingly revised their own readings at some point, because these look to be superior to what's currently on the DB. Three further Korean areas of interest: Koraiyama and Nankaiyama - both recruited in the same year by the same stable, but one has his name transcribed with a Korean reading and the other with a Japanese one, even though both look pretty Korean in structure. I suppose it's possible given the convoluted history of the early and middle 20th century, but is that accurate? Ozora - I don't know what to make of this: the Kyokai now lists his real name as OZORA Juei, rather than the previously listed SHIMODA Juei (which is also on the DB). The shikona was adopted in 2015.09, and the apparent (second) real name change took place at (or around) the same time - the rikishi directory with 2014.11 data still had him as Shimoda, the one with 2015.11 data says Ozora. Still, this seems like a weird thing to have happened. Yamada - Wikipedia lists a Korean name "YU Sonyon" - I don't know where that was sourced, anyone?
Philippines (4) Kotokuzan (Filipino origin, JP shusshin) - Wikipedia reminded me that Filipino newspapers have given his full name as Jasper Kenneth ARBOLADURA TERAI - I'm correct to assume that Arboladura is a surname, right?
Russia (6) - Languages based on the Cyrillic alphabet are not exactly my forte, so other opinions very welcome. Roho and Hakurozan - I think a better transcription of their middle name would be Feliksovich, which seems more accepted and is also what the Kyokai lists. (Not sure if the DB's -sevich originated there or elsewhere.) Wakanoho - Possibly better Aleksandrovich. Certainly -vich is more common than -vitch, not sure if -ks- is preferred over -x-. The Kyokai has the -ks-vich version.
Sri Lanka (1) Tochitaikai - Wikipedia gives his name as "Sri Aminda de Perera" - I don't know which parts of that are the surname (just DE PERERA oder AMINDA DE PERERA?), and while I also don't know if it's actually correct, that reading looks a lot more plausible than the DB's current version.
Taiwan (11) Ohayama - same issue as with Kanoyama among the Chinese rikishi. This guy has the non-simplified version 葉 of the same kanji, and in this case there really doesn't seem to be a way that this could possibly be read XIE. Should probably be changed to YE, unless somebody has superior insight. Other than that I don't know enough about how Taiwanese name readings might possibly differ from "standard" Chinese, so it would be best if somebody else checked out the 11 rikishi entries.
Tonga (8) Fukunoshima - full name Tonga 'Uli'uli FIFITA, per Wikipedia. (Not sure though if the two apostrophes should be included in the DB name entry, or if Uliuli would be sufficient.)   Hidenoshima - Doesn't anybody have anything more than "Shioeri"? Sachinoshima - his surname was already added a while ago, but might be worth also listing his middle name Havea, per Wikipedia. Tomonoshima - Wikipedia gives his name as Viri Manulea FIFITA (rather than the DB's Manurea transcription). Yashinoshima - Wikipedia gives his name as Moleni Fe'aomoeata TAUKI'UVEA, no idea about the source. Minaminoshima the father - full name Tevita Vaiola FALEVAI, per a Kyodo/Japan Times article from 2015. (Note, Tevita rather than Tebita.) Minaminoshima the son - names are in the wrong order, should be Minaminoshima Isamu FALEVAI. (By the way, apparently the father later competed in at least one early sumo world championship?! Bronze medal in the 1996 open weight according to that page, must have been 41 at the time.) Aotsurugi - debuted at the same time as Minami the son, so his name listing at the Kyokai probably follows the same structure. I think that means his name should be listed as Tevita Ratu TAUFA. Based on Minami the father I'm assuming that the proper spelling of that Tongan name is Tevita, not Tebita. In addition, I'm suggesting Ratu instead of Rato because the printed rikishi directories give his name as ラトゥ, not ラトウ. (That would need to be corrected for his Japanese entry as well.) Also, should his naturalized given name be adjusted to "Tevita" as well? 
Western Samoa (2) Nankairyu - the correct name appears to be Kilifi SAPA. Referred to as such occasionally in the Hawaiian newspapers of the time, and a Guam newspaper has some 2015/16 articles with somewhat unsavory news for someone of that name (and the age matches). Nanyozakura - no luck finding anything about him. Wikipedia has his given name as Faaleva, but I don't know the source for that.
  Nothing to note by me, but might be worth a look anyway: Bulgaria (3)
Czech Republic (1)
Great Britain (1)
Hong Kong (1)
Hungary (1)
Indonesia (1) 
Kazakhstan (1)
Paraguay (1)