Done. Let the game save once (auto-save, or OPTIONS > MEMORY CARD > SAVE) and the unlocks stay after you turn the code off.
Only some characters or modes
the matching Unlock ... codes
Same as above.
The "earned over time" content
Max play time
Open the GALLERY once. That runs the game's own play-time check, which grants every time-released unlock.
A stage that never appears in the carousel
Stage select: hidden stages too or Load any stage
Use it in Training or VS mode stage select.
Caveats
These are for SLUS-21847 (CRC F233A433) only. The PAL, Japanese and Plus R discs use different addresses.
The save-data codes are permanent once the game saves. Back up your memory card if you want to keep a clean save.
The stage-select codes only affect the stage-select carousel (tested in Training; VS modes use the same screen). Arcade, Story and
M.O.M. choose their own stages.
Load any stage holds the cursor on one stage, so the carousel cannot move while it is on. Stage table entries
19 (Korea), 35, 36 and 39 hang the game. 59 is the table's empty terminator row and hangs too.
Unknown flags: the bytes at +0x259 ... +0x26D are set by the debug routine and included in Unlock everything,
but we found nothing that reads them in a visible way.
Setup steps for PCSX2 and cheat devices: How to use.