'Mong' is short for 'mongol' so is an outdated and pejorative term for people with Downs Syndrome.
Both it and 'Spaz' are definitely very offensive here in the UK, I think an equivalent might be describing with physical disabilities as a cripple. They are not terms, here, which would be seen as 'outdated but part of normal vocabulary for the general population' as opposed to people within specific communities, or where you'd be getting eye-rolls for being offended!
It's interesting that the terms haven't fallen out of use in the US - is it still the same with the terms '*******' and 'retarded'? I've never come across '*******' as anything other than a pejorative here in the UK, but I understand it was used officially / descriptively in education in the US until fairly recently (not sure whether it is still used in that way)
(On a similar note, 'handicapped' has fallen out of use here - it's much more usual to hear people described as having disabilities, and things like parking spaces and permits are described that way. I think 'handicapped' is a term which would be seen more as outdated than offensive, in the general population, however)
At least in education terminology, it's a bit of a divide. The original legislation which allowed intellectually disabled to come into public schools refers to them as "mentally retarded". However, when learning about disabled children as a music therapy student, we're instructed to use person-first terminology, such as "person who is blind" or "person who is intellectually disabled". We're also asked to use terms such as intellectually disabled.
Now this is interesting, as it goes against some aspects of newer Critical Disability Theory for me. I have a disability and I used to hear the "person first" language, but newer advocates have been trying to "take back" the language. (FYI, I am also in education at a high level) This means saying 'disabled person'. The idea appears to be, and I am not an expert in Critical Disability, that you would not say "someone with gayness", you would say "gay
person" or so on, so why should disability be treated as something outside of your identity?
In specific situations, I do identify as a "disabled person", as to me, I am taking back that label as it is part of my identity.
This is merely an aside, as I find it interesting.
PD Story: Years ago, I worked in administration under a manager who, to this day, I am not sure how they got that job. It was entirely computer-based, with specific programs that were only used in our industry. Did the manager know how to use/access these programs? No. Did they know how to use Word and other standard microsoft programs? No (not even Explorer, which I was pretty shocked by). They did know how to use their phone though, and talk at length about what they had been eating throughout the day, and whether they were adhering to their diet.
I changed industries after working with that manager for a year. They weren't too bad, but the lack of basic computer skills meant that our department got little done, as they couldn't properly manage or coordinate what was going on. (I just remembered that that manager couldn't understand their email either. Standard outlook). The manager also wasted a large amount of time not only on the phone, but also through getting me and my coworkers to continuously show them how to use their computer.
I was always pretty confused about how they could not have that basic basic knowledge, or at least make any effort at retaining what they were shown. It seemed like a pretty silly thing to not know how to do, and to not make any effort to learn, particularly as a manager.
They're still working there.