Fun fact: PSP emulator is still having a lot of backdoors that are not patched.
Vita mode is also having some serious problems with me. When playing Unit13 the game stuck a lot of times on loading a save-game. Also when you eject the game and push the PS button it will start to blink. I cannot get it to work anymore. I let it run dry on battery but when i switch it on the PSVita still has black screen and a blinking PS button. So i guess we can do something with that. Time will tell... Unfortunately i cannot help because of the blinking PS button.
EDIT: Don't panic. To save the PlayStation Vita from the blinking blue light of death, hold the On/Off button located on the top of your Vita for about 30 seconds. Your Vita will boot into a debug menu where you can choose to start it up normally.