
Alright, I'll try and make this post as short and snappy as possible.
Fact #1:
A lot of producers don't care about how their sounds play back in mono OR they don't know how to check/fix/address it.
Producers should know about this โ unless they work with an engineer that points this out to them and tells them how to fix it (when I master music, I cannot fix it, but if I mix or stem master it, I can โ and in mastering, I tell the producer if he has to fix it).
Good news:
It's very easy to check and fix.
So what is mono compatibility?
It means that sounds are strong/loud (enough) in mono.
There's lots of sounds out there that are wide but they're not necessarily loud enough in mono. Not all sound designers are audio engineers: many of them make sounds like synths, pads, FX etc really wide to impress you, but watch out for how they play in mono.
Why should the sounds be strong in mono? Doesn't everyone have a stereo system?
Basically, we hear in mono a lot of the music we hear when we leave our house and which we don't hear from our trusted system at home or headphones.
Clubs, cafes, restaurants, public transportationโฆyou name it.
You're very rarely positioned between two speakers, when you'd experience the sound in stereo. A lot of clubs are in mono, technically, for the reason I just mentioned.
A real-life scenario would be you playing your song that has a nice, wide vocal in a club and realizing it's now too quiet; poor mono compatibility is the reason!
Fact #2:
Really wide doesn't guarantee that the sound has decent mono compatibility.
Fact #3:
Really wide and really strong in mono are not mutually exclusive.
So how do you check it?
There's two ways.
๐ Mono check method 1: Listen โ nothing to see here!
Have on your master (or on the track that has the sound you want to check in mono) a plugin that makes the sound mono (e.g., a stock DAW plugin that makes width 0% etc โ if you need tips on this, just comment, but I'm sure all DAWs have these plugins).
Flick it on, and listen. If the sounds are loud enough in mono, good. If you notice that some sounds drop too much in level, the sound could be better in terms of its mono compatibility.
So how to fix this?
There's two ways I use.

Have the free Voxengo MSED plugin on the track (not master!) that has the sound we want to fix โ e.g., the sound that isn't loud enough in mono while it's nice in stereo.
The plugin has mid gain and side gain (as seen in the pic above). What your sound needs is mid gain. Flick the sound (or master) to mono, and keep raising the mid gain of the sound till it's loud enough in mono.
Booom! You've made it loud enough in mono.
(A question would be, "Why not just raise the track level?" and the answer'd be "Well, if it's already loud enough in stereo, that method will make the stereo (or the whole sound) appear too loud. We already established that it's nice and wide, remember?)
Instead of SPAN, have a stock DAW plugin on the track that can control the width of the signal (e.g., in Ableton Live, it's "Utility" and in Bitwig it's "Tool". Take the width all the way down. Then raise the level till it's loud enough (it's mono as you do this), and once it is, restore some of the width back to taste.
Boom, done!
๐ Mono check method 2: Looking at phase correlation meter.
I rarely use this, though, as I do listening checks ALL the time, and hearing is more important than seeing. But I know some ppl are very visual beings, so hey, this can help.
Use a phase correlation meter such as free Voxengo Span.


See the two pics above. See the horizontal meter on the bottom right. See the difference between those two pics? In the upper pic, the meter is leaning slightly left of middle, where on the lower pic, that meter leans more to the right.
In a nutshell: the more it leans to the left (of center), the poorer the mono compatibility will be. The more it leans to the right, the better the mono compatibility is.
And this refers to checking a sound, not the whole song (it's hard to tell about a sound's mono compatibility when everything is playing).
If you find sounds in your song that seem to be leaning a lot to the left, try monoing it, and you will hear, that it loses a lot of level in mono.
When you have a stereo sound, it'll always flicker a bit even when the mono power is good, so don't expect it to stay fully on the right (that only happens with fully mono sounds).
Well, that is it!
TL;DR recap: have a mono-maker plugin on your master, check the song in mono, and if sounds that are nice and wide suddenly appear too quiet in mono, fix them with a plugin such as MSED by raising the mono gain of the sound (not the master)!