I've just finished packing up R13 and uploading it to sourceforge:
Daedalus PSP R13 for v1.00 Firmware
Daedalus PSP R13 for v1.50+ Firmware
Daedalus PSP R13 Source
The most significant new feature is savestate support. You can now save your progress at any point, via the Pause Menu (accessed through hitting the Select button). Savestates are written out to the memory stick, and consume around a megabyte per slot. You can load up a savestate at any time from the Pause Menu, or via the front end (hit the right shoulder button to swap from the rom list to the savestate list.)
Other than savestates, the most significant change in R13 is a number of optimisations to the dynarec core which should give a 10-20% speedup depending on the title being played. I've tested these optimisations as much as I can, but if you find that roms which worked with R12 are now broken, try disabling 'dynamic recompilation' and/or 'dynarec stack optimisation' from the rom's preferences screen.
I haven't looked at compatibility at all in R13, so it's unlikely that any roms will have started working in R13.
I'm interested to hear your feedback on both of these features. Let me know if you have any problems with savestates, or if you've found roms are no longer working in R13. I'll try and keep on top of the comments pages over the next couple of weeks.
It's taken a LOT longer to get R13 out than I had hoped. I can't quite believe the last release was in June! I'm hoping now I've got this release out of the door I'll be able to get back to making small, more frequent releases.
Update A couple of things have cropped up in the comments. Firstly, when you create a savestate it can take a while - up to 10 seconds - during which time the screen is black. It will complete though - please be patient :). I'll have a look at adding a progress meter or something like that for R14.
There are a few titles that don't seem to be working well with some of the dynarec optimisations I added. If you're having problems, try turning off the 'dynarec stack optimisation' as discussed above.