I think some "compare and contrast" with the English expression would help.
I think the main problem is that "more or less" does not mean that in English; it means (per Wiktionary) either "approximately" or "almost". It doesn't work to combine this with an unspecific modifier such as "high", "many" or "large"; you wouldn't say "approximately large" or "almost large".
The expression is covered in the DWDS entry under mehr and they give the definition "in bestimmtem, gewissem Maße" = "to a certain extent/to some extent". It's also covered in the entry for minder, but there they only give examples with no definition. One of the examples is "mit mehr oder minder großem Erfolg".
From the examples I've seen, I think the best translation would be "to varying extent" or "to some extent" depending on the situation. For example (from Die Ziet via DWDS)
Nach Schätzungen ist jeder zweite Deutsche zwischen 52 und 64 Jahren mehr oder minder stark von dieser Linsentrübung betroffen; in der Altersgruppe ab 65 Jahre wird sie sogar bei 90 Prozent aller Menschen vermutet.
According to estimates, every second German between the ages of 52 and 64 is affected by this clouding of the lens to some extent; in the age group from 65 years it is even suspected in 90 percent of all people.
I'd like to note as well that "more or less" is common in spoken English, while "mehr oder minder" seems to be more common in written German.
Also note that these are fixed expressions, not quite idioms but also not to be taken too literally. German and English seem to have changed the literal meaning in different ways and this seems to be the cause of most of the confusion.