Mismatched disk/drive refers to, for example, reading/writing a 720K disk with a 1.44M drive.
Don't forget LS-120 and LS-240 SuperDisk drives, they can use standard floppies too.
What can and can't be read/written with a given drive type?
I’ll limit my answer to common 3.5” formats on PCs, DSDD, DSHD, and SuperDisk, as listed in your question.
SuperDisk drives can be ignored as far as backwards-compatibility is concerned: they have two head assemblies, one for “standard” formats, the other for LS formats, and the “standard” head is equivalent to a high-density 3.5” drive’s.
The main concern with non-LS 3.5” floppies is the metal used in the medium. DSDD and DSHD floppies use different metals, with different coercivities. HD drives can adjust their field strength to write appropriately, so an HD drive can write to a DD floppy without creating issues. Problems arise when using a DSHD floppy in a DD drive: it is possible to format a DSHD floppy using a DD format, but if the floppy was ever formatted with an HD format (or was pre-formatted, as was common in the late 90s), a DD drive won’t be able to correctly reformat it (because its write signal isn’t strong enough). Problems can also arise when overwriting data on a DD-formatted floppy using an HD drive; it’s always better to “write from blank”.
The basic rules of thumb for 3.5” drives are:
Exchanging data with non-PC systems can be more complex (especially with Macs and Amigas), and in such scenarios it’s often better to stick to PC formats for data transfer.
Using non-standard formats in PCs (as produced e.g. by
FDFORMAT or 2M) can introduce compatibility problems too, and they should generally be avoided for transfer between systems (unless you also transfer the drive that formatted the disks).
Below I don't discuss the issue of single-sided versus double-sided drives since it seems sufficiently obvious. Also, when I say "PC" I'm refering to common western IBM PC-compatible computers.
Amongst commonly used floppy drives, there are only three basic types you need to worry about. 3.5" drives are essentially smaller versions of 5.25" drives, so the issues are the same for both types.
As Stephen points out, there are only two types of media: "double-density" (which is actually the same as single-density media) and high-density. These have different magnetic properties and, while DD drives may be able to write on HD floppies and vice versa, this will be extremely unreliable at best.
HD drives almost invariably support writing to DD formats as well. This is automatic in the case of 3.5" HD drives (via the second hole in the corner across from the write-protect hole); for 5.25" HD drives you must manually specify DD format (though the OS may check and do this for you, except when formatting diskettes). However, HD drives are also invariably 80-track drives, and will have the same issues with 40-track interchange as 80-track DD drives.
The issue between 40- and 80-track drives is that the 80-track drives use a narrower head and read/write a narrower track. Thus an 80-track drive will read a 40-track diskette produced by either type of drive with no problem. However, a 40-track drive will generally have great difficulty reading any sectors (or full tracks) written in 40-track format by an 80-track drive. (Many retries may eventually produce a successful read.)
As Stephen also points out, the LS drives are are a completely separate thing with their own heads, and so not really relevant for interchange.
¹The oldest models of these drives used only 35 tracks, but are otherwise compatible so long as you don't try to access the additional five tracks used later. Even into the '80s some drive systems, such as the Apple II and Commodore 1541, used only the first 35 tracks though the drives themselves were capable of accessing all 40 tracks.
²Yes, there are 3.5" DD 40-track drives. They were quite rare in the (western) PC world, but not uncommon elsewhere, such as in Japan. I own several, and have data sheets.