"I like people."
Translation:Ich mag Menschen.
The connotations are slightly different. Menschen goes into the direction of human beings, Leute is more like folks. In most cases they can be used interchangeably. However in this case Menschen sounds slightly better to my ears.
"Leute mir gefällt." Gefallen is more like "is to my liking"
"Leute gefallen mir. " or "Mir gefallen Leute." are the correct versions.
The subject and direct object are interchangeable, by my understanding, so the example given was valid. That said, it would read awkwardly or even archaically when inverted
Is there any difference in meaning between 'ich mag Menschen' and 'ich mag die Menschen'? Is the second more specific about which people you like?
Personally I prefer "ich mag Menschen" because I don't have to remember the "the" article. I also hear people use that phrase more often. I think it's the same differentiation between "I like people" and "I like the people" same as English. Not 100% certain though
So now I can finally say, "Ich mag Deutsch Menschen" and "Ich mag Deutsch Frauen" without sounding affectionate. I heard some European cultures aren't emotional or buddy-buddy like my region.