There are currently no missing addr:city Post Town values for any objects with DE or NG postcodes https://osm.mathmos.net/addresses/post-towns/
Outside of the centres of post towns I've often added addr:suburb, addr:village and for Wirksworth (addr:city = Matlock) and Castle Donington (addr:city = Derby) addr:town. Am fairly relaxed as long as addr:city is populated. I sometimes add addr:hamlet and have seen addr:locality or addr:suburb used generically

Wrong changeset description. Connecting car park to service road, not construction.

I have restored a Derby address for this vacant building way/111606077 and have added Presentation Design Services to the map in the new location with a Somercotes, Alfreton address node/12559311347 added as a point/node to make it easy to correct if I have not added at quite the right location

https://osm.mathmos.net/addresses/pc-stats/NG/NG7/2/ where a cluster of NG7 2EB postcodes near the NG7 2DZ centroid shows as location discrepancies for both

Or possibly motor_vehicle = no @ Sa-Su 00:00-04:00 for The Strand

These "opening_hours" don't seem appropriate. The Strand is closed to vehicles in the early hours of Saturday and Sunday mornings to enhance pedestrian safety. Perhaps motor_vehicle:conditional = no @ Sa-Su 00:00-04:00
Wardwick remains open to traffic I think including for Taxis picking up on Victoria Street and cars parked in the Saint James's Street Car Park I presume,

The bridge has been temporarily swung to to the riverbank to allow the waters to rise and so is not open today but will be swung back into place soon.

Please revert this deletion. The bridge exists https://en.wikipedia.org/wiki/Cathedral_Green_Footbridge and is visible in aerial images.
Updated note/4571374

I've removed all old_fhrs:id values in the Derby City Council, South Derbyshire and Erewash areas and a few others near Derby in Derbyshire Dales and East Staffordshire (Burton-on-Trent)
I've left Amber Valley alone as they tend to reuse numbers and have also left Broxtowe and Nottingham for the Nottinghamshire community to review

Looks like the Corn Market shop way/127881176 is still open and the Albion Street one has closed node/5345389260

I've added a noexit tag to the end of John Street node/441401666 and have also added the Lidl car park way/1340039157
Unsure which of the Mansfield Road postcodes to use as Amber Valley Food Standards uses DE55 7JL https://ratings.food.gov.uk/business/605/lidl and Lidl DE55 7JJ https://www.lidl.co.uk/s/en-GB/store-finder/alfreton/mansfield-road-18/ but it should not matter as neither of these are on Nottingham Road or John Street so would expect navigation via Mansfield Road

Excellent work on adding postcodes https://osm.mathmos.net/addresses/pc-stats/DE/

DE55 Alfreton had previously only had a few postcodes added from Amber Valley Food Standards and for existing objects from Code-Point Open centroids so is now much improved

If possible please add addr:city for the relevant post town Alfreton, Ashbourne, Burton-on-Trent, Derby, Matlock, Ripley, Bakewell, Ilkeston, Swadlincote and Belper only https://osm.mathmos.net/addresses/post-towns/DE.html for DE postcodes

Sometimes useful to add addr:suburb, addr:village or addr:town https://osm.mathmos.net/addresses/addr-tags.html although I have only ever used addr:town for Wirksworth (DE4 addr:city = Matlock) and Castle Donington (DE74 addr:city = Derby)

I would not normally add postcodes for non-geographical (PO Boxes etc.) postcodes like node/12335209625 flagged as “Multiple Units at the same location (ML)” and excluded from the statistics https://osm.mathmos.net/addresses/pc-stats/DE/DE55/4/ but is probably harmless to do so

As recently as December 2023 Companies House recorded an address change for Faux from 608 to 579 Mansfield Road although this could just be a correspondence address for an online business https://find-and-update.company-information.service.gov.uk/company/13175837/filing-history
08 Dec 2023 Registered office address changed from 680 Mansfield Road Nottingham Nottinghamshire NG5 2GE United Kingdom to 579 Mansfield Road Nottingham Nottinghamshire NG5 2JN on 8 December 2023

Without checking on the ground I assumed Faux must have moved across the Mansfield road from 608 to 579
Both Faux and Pudding Pantry are listed at 579 for the postcode https://ratings.food.gov.uk/authority-search-landing/899?address-search=NG5+2JN&business_type=-1&hygiene_rating=all&range=Equal (no date of inspection for Faux)
If Faux is closed then would be easy to tidy just leaving Pudding Pantry

DE Post Towns https://osm.mathmos.net/addresses/post-towns/DE.html

Excellent work on adding postcodes https://osm.mathmos.net/addresses/pc-stats/DE/ DE1, DE4, DE5, DE45 and DE72 should be showing 100% when the statistics are next refreshed.
If possible please add addr:city for the relevant post town Derby, Matlock, Ripley, Bakewell etc.
Sometimes useful to add addr:suburb, addr:village or addr:town https://osm.mathmos.net/addresses/addr-tags.html although I have only ever used addr:town for Wirksworth (DE4 addr:city = Matlock)

I've no objection to this being updated to variety_store and perhaps way/133732739 in Derby also needs updating
I don't know the detail of Cushty Bargains but the variety of goods sold must include some foods https://ratings.food.gov.uk/business/1520728/cushty-bargains

In July 2022 I incorrectly updated the 25 Underhill Close house to a Go Local Extra based on the 30 June 2022 Food Standards entry https://ratings.food.gov.uk/business/1526762/go-local-extra-derby now reverted and mapped as a terrace house again way/630957133

Thanks for fixing the duplicated cottage name way/662674262
Not sure if the Ordnance Survey can be asked to update their OpenMap to match "Tithebarn" as they are often used by Google, OSM and others as the master
I was not consiously surveying this afternoon but I cycled past a "Tithe Barn Gardens" in Repton way/966866953 and "Tithe" is the spelling I would expect for 10% of income or a 10% of a harvest donated
Your sources and edits look good

Probably needs checking on the ground.
OS OpenMap Local (April 2024) suggests "Tythebarn Lane" (one word with a y) and there is a "Tythe Barn Cottage" (two words with a y) way/662674262 (and another "Tythe Barn Cottage" way/662674259 which may also need checking as it seems unlikely that there are two cottages with the same name