This is interesting! I discovered a yearor so ago that a boggy area where we used to collect frogspawn as children (the other side of the disused railway) is known to today's local children as the Fairy Pond.
I think you should add a description giving an idea of how local the name is ("Reservoir known very locally as. . . " or something.)

I'm pretty sure the area between Harrogate Road and the golf course isn't a common, as it has a big sign up saying it's a playing field belonging to St Elisabeth's School. See osm.wiki/Leisure%3Dcommon for an explanation of what the tag is meant to cover.

The aerial view of the glassworks is somewhat misleading—it looks as though three corners are truncated, but at ground level only two of them are.

PS it looks as though St Joseph's also has the whole site marked as being a building. The way to fix that is to remove the building=yes tag from the site outline. Then if you want, draw the actual building and tag that with building=church.

Thanks for giving some attention to Reddish. I noticed that the entire Christ Church site was tagged as a building (maybe by the preset in the editor), so I've corrected that and moved your address tags to the actual building. Also Lillian Grove had become attached to one corner of the site, acquiring a bend, so I've straightened it out again.

Um, "North" not "Nothing"! That's predictive text for you.

"Partial survey" because today I only walked around three sides of the area (the Fovant Crescent part) and couldn't see any obvious access to the reserve, just that there were trees behind the gardens. So I wasn't able to check properly what's there. From the aerial view it looks like dense trees.

Here are the wiki pages for the two:
leisure=park
leisure=nature_reserve

It's important to note that the name= tag is just meant for actual names, not descriptions.

Also, in the few months I've been mapping, I've found that it's sensible to always search the Wiki before mapping a feature I've not previously done. Often there turns out to be a specific tag for it that I didn't know about, or some pitfall to avoid which I would have walked straight into.

The wiki start page is at osm.wiki/Main_Page

Correction: Harrogate Road ones were in the previous edit.

Sorry, that should be houses 542–544. Vespucci doesn't let me see the map at the same time as writing a changeset comment.

Or rather, 74-78

Cotrection: the source was the Manchester Council page for the allotments, at http://www.manchester.gov.uk/directory_record/106024/levenshulme_allotments