Please note that this is just an overview and does not mention or explain every new feature.
The following is a (probably incomplete) list of changes made between the 3.12 and 3.13 release of MorphOS to the ROM (boot.img) based components.

Quark
- Fixed issues with Pegasos II shutdown
- Fixed several issues related to the Pegasos I OpenFirmware support
- Improved Sam460 support in 'SATA' mode
- Silenced some debug output
- Added FD=FWDebug boot argument for Pegasos I/II systems as well
- Fixed issues with proper identification of PCIE PowerMac hardware and its registration support
Cybergraphics
- Stability improvements
DOS
- Improved RunCommand() state preservation and restoration
- Refuse to boot an ISO that has newer MorphOS version on it
- Fixed the boot code possibly picking a non-bootable device in some rare situations
- Fixed a potential crash in CreateNewProc() error code path
Exec
- Improved ColdReboot/ShutdownA handling
- Fixed floating point rounding mode preservation
FatFS
- Fixed a zero-page hit in ACTION_REMOVE_NOTIFY
FFS2
- Fixed bugs related to default filesystem usage
Graphics
- Fixed a use after free bug
- Fixed potential race condition bugs
Intuition
- Authentication screen's window cannot be accidentally iconified anymore
- Fixed authentication screen resource leak
Log
- Improved to show segment information for 68K exception program counter address
- Improved FPSCR register display
PFS3
- Fixed softlink support when link points to ":name"
- Fixed a harmless off by one bug in softlink support
Powerbook
- Fixed num lock led controls on some keyboard models
Ramlib
- Fixed a bogus library version for the OldOpenLibrary call when debug was enabled
Following is a (probably incomplete) list of changes made to the disk based components of MorphOS.

Ambient
- Disabled wallpaper transitions on hardware with too little video RAM
- Reduced overall video RAM usage
- Fixed a race condition resulting in a crash when modifying icons

Applications/FlowStudio
- Added gcc9 and g++9 compiler defaults
- Fixed text measurement problems on startup when TTE rendering is enabled
- Fixed jumping to functions with prototypes longer than ~90 chars
- Tasks that were completed with single stepping could not be restarted in the debugger
- Make sure that at least the 'MUI skin' option is always available, for instance if the Skins directory couldn't be found
- Sets the correct PROGDIR for the debugged process

Applications/Odyssey
- Updated the root certificates bundle
- Updated to more recent cURL library
- Fixed user style sheet load issue
- Other minor fixes and improvements

Applications/Jukebox
- Character encoding fixes
Applications/RDesktop
- Fixed AHI audio related issues
Applications/Showcase
- Fixed some busy looping bug in image browser thumbnail scanner if delayed scan wasn't enabled
Applications/Transfer
- Stability improvements
- Added missing UTC time conversion for FTP download
Applications/VPDF
- Updated poppler library to 0.85.0
- Fixed a Freetype related memory leak on close

C/Iprefs
- Improved detection and reporting of booting the system with a wrong boot.img
C/PowerMac7FanControl New
- Tool for controlling the fan speed and reporting fan status and system sensor temperatures on PowerMac7 systems.

Classes/Blankers/PicView.btd
- Worked around the issue of screen going blank after a while
Classes/Frameworks/mui.framework
- Fixed MUIString overloaders using String.mui instead of StringU.mui
Classes/Frameworks/ob.framework
- OBArexx now works with old rexxsyslib.library versions
Classes/Mui/Scintilla
- Fixed a zeropage read hit
- Implemented support for subpixel TTE font rendering
Classes/Reggae/gif.demuxer
- Added missing MMA_MediaType handling
Classes/Reggae/netpbm.demuxer
- Added missing MMA_MediaType handling

Devs/Monitors/Radeon
- Filter out resolutions that are provided by the connected monitor but can not be displayed by the connected graphics card output
- Refuse to generate DualLink DVI output resolutions on R100/R200 family GPUs
- Fixed iMac iSight dual head support
Devs/Monitors/SM502
- Fixed displaying 16-bit modes
L/Apipe
- Support for querying the amount of pending data in the pipe
L/SmbFS
- Fixed a possible hit once the (optional) user/password window was closed on mount
L/Ssh2fs
- Statibility improvements

Libs/Cairo
- Fixed a possible memory leak related to unfreed Freetype/Font resources
Libs/Cryptostorage
- Added new functions: CryptoStorageClear(), CryptoStorageExport() and CryptoStorageImport()
- Improved debug output
Libs/Diskfont
- Disabled some unused code
Libs/Freetype
- Added support for configurable hinting mode
- Fixed anti-aliasing issues with new freetype.library
- Improved harfbuzz.library integration
Libs/Harfbuzz
- Fixed several potential lock-up issues
Libs/Ixemul
- Fixed lseek64 function return value for seek positions >2GB
- Added pread/pread64/pwrite/pwrite64 functions
- Optimized lseek/lseek64 function
Libs/PNG
- Only open locale.library on demand
Libs/PPC
- Improved FPSCR register display
Libs/Realtime
- Fixed the version tag
Libs/TTengine
- Added support for configurable hinting and anti-aliasing mode
- Implemented RGB sub-pixel anti-aliasing
- Implemented highly optimized rendering routines
- Fixed several memory corruption bugs and race conditions
- Implemented TT_PrintMode
- Fixed mixed font size issue

Default UI Skin
- Default Ferox Skin has been replaced by the retro-inspired Origo skin, which had been first introduced in MorphOS 3.10
Devs/Networks/p50x0_eth.device New
- Driver for onboard GbE controller of the P50x0 A-EON boards
Fonts/_ttf
- Updated RobotoMono font with correct fixed width information
MUI
- Account for text format spacing even if the actual object isn't there. Fixed Listtree arrow-text spacing
- String.mui: Additional checks in OM_SET against trying to do RastPort related computations while not shown
- String.mui: Fixed a cursor position check
- Disabled LCD AA for regular MUI text to be consistent between MUIA_Unicode modes
- Shuffled some early initialisation code around to avoid a random boot hang
- Fixed Unicode support in register group titles
Network/Netstack
- DNS resolve operations can now be aborted
Prefs/Font.mprefs
- Added support for configurable hinting and anti-aliasing mode
Prefs/Preferences
- Minor UI improvements
Skins/Origo
- Added some additional sizes to qualify as new default UI theme
Tools/FTManager
- Fixed a crash with anti-aliased font preview
Utilities/Grabber
- Fixed to work when Reggae classes are not already loaded
Tools/IWizard
- Protected Install/Update button against being enabled again while an installation is running
- Only tries to mount HFS partitions that are writable
Utilities/Multiview
- Fixed selection of unicode fonts for text and guide display in settings