People have added 69 sections under Genus Begonia but there's still:
a) Its unclear if these sections have all the species assigned to them that they should have. 341/960 species grafted directly to the genus. If any of these should be moved to a section please help do that
b) there's no references on where these sections and the species they contain came from - if anyone can provide any references please do so here

Thanks!

I've linked to this flag from a deviation where I'm accounting for the Sections here https://www.inaturalist.org/taxon_framework_relationships/466308

I have created the sections and added/sorted many species, but i need more time/help. There are well over 2000 described species and the genus keeps on growing fast with several new species each year.

There are lists, but in order to see if the allocation to the respective sections is correct, I often have to check the species individually in the more recent scientific literature.

Nearly all of the species not yet assigned to a section on iNaturalist must be checked and moved to a section.

Today I updated sect. Tetraphila. I moved existing species, added missing species, subspecies and varieties, maps and synonymes.

I sorted some species into the sections according to https://padme.rbge.org.uk/Begonia/home
but the following species are not listed in this site:
• Begonia buimontana
• Begonia huegelii
• Begonia lucerna
• Begonia rex-cultorum
• Begonia semperflorens-cultorum
• Begonia vincentiana
• Begonia vulgaris
• Begonia × albopicta
• Begonia × hiemalis
• Begonia × ricinifolia
• Begonia × taipeiensis
• Begonia × tuberhybrida

Hi @t_e_d

Begonia buimontana should be renamed Begonia × buimontana Yamam. to be correct in iNat. (https://powo.science.kew.org/taxon/urn:lsid:ipni.org:names:104335-1) @hfb can you do this, please ?
Begonia huegelii is recognise in POWO and Padme (https://padme.rbge.org.uk/Begonia/Data/nomenclature?padme_species_epithet_s=huegelii). No problem.
Begonia lucerna should be renamed Begonia 'lucerna', but cultivars are not accepted in iNat database. However this entry is VERY usefull to ID many casual/cultivated begonias (for the present iNat tolerates non-wild plants as well), so I don't think it's a good idea to ask for it to be deleted.
B. rex-cultorum and B. semperflorens-cultorum are both horticultural groups. Idem, cf. B. lucerna.
Begonia vincentiAna is a spelling mistake. Look for Begonia vincentina in the databases.
Begonia vulgaris is recognised in Kew and padme (https://padme.rbge.org.uk/Begonia/Data/nomenclature?padme_species_epithet_s=vulgaris). No problem.
The five last hybrids, natural or not, are accepted in POWO, so it's ok in iNAt.
Hope this answers your questions.

When it's possible, Padme-RBGE or WFO mentions the section.

I have sorted 42 species into the sections.

Species not sorted :

Begonia cunhambebei is missing on Padme, and unplaced by WFO ;
Begonia lucerna which should be Begonia ʽLucerna’, a cultivar (not allowed on iNat) : see https://www.inaturalist.org/flags/527291 ;
Begonia rex-cultorum which is a Group (not allowed on iNat, and should be flagged) ;
Begonia semperflorens-cultorum which is a Group (not allowed on iNat, and should be flagged) ;
Begonia ×albopicta = Begonia maculata × Begonia olbia, but Begonia maculata is in Begonia sect. Gaerdtia and Begonia olbia is in Begonia sect. Latistigma ;
Begonia ×hiemalis = Begonia socotrana × Begonia ×tuberhybrida, but Begonia socotrana is in Begonia sect. Peltaugustia and Begonia ×tuberhybrida is in Begonia sect. Australes.

Note :

Begonia fernandoi-costae is misnamed Begonia fernando-costae by Padme, and by WFO

@begalma :
https://www.ipni.org/n/30542-2

Nomenclatural Notes
as Fernandoi Costae

No need to change that name according to the Code, see : https://www.iapt-taxon.org/nomen/pages/main/art_60.html

I have sent a feedback to IPNI about Begonia fernandoi-costae.
Done for Begonia cunhambebei.
For next time, can you give the links, please ?

Hi, @t_e_d Begonia albo-picta [sic] is placed in Section Gaerdtia in Tebbitt, 2005.

The same plant has been named Begonia albo-picta W. Bull (Tebbitt 2005), Begonia albopicta W.Bull (IPNI), Begonia × albopicta W.Bull (POWO), etc.
Anyway, as far as I know, Begonia Sections lists are only available at species rank, therefore it seems doubtful to me to classify hybrids in this way, even from two parents in the same section.

Yes, but that's no the point. The reference bases do not allow us to make out the section for new hybrids, even with parents in the same section, unlike other species. Exemples :

Begonia × chungii in POWO (https://powo.science.kew.org/taxon/urn:lsid:ipni.org:names:77099695-1) is absent from Padme, and WFO do not mention the section for Begonia chungii (https://www.worldfloraonline.org/taxon/wfo-0000915270).
Begonia × taipeiensis in POWO (https://powo.science.kew.org/taxon/urn:lsid:ipni.org:names:1015312-1), is absent from Padme, and WFO do not mention the section for Begonia taipeiensis (https://www.worldfloraonline.org/taxon/wfo-0000825698), etc.
Can iNat invent it if the taxonomists don't ?

These restrictions do not apply to the examples above

As I have already told ("even with parents in the same section") : the above exemples have both parents in Sect. Platycentrum, but have no section in WFO. You can follow the links if you don't believe.

Not to me.