I really really don't know. I have had a PSP since launch and I really don't play it that often, I just save it for long trips, though it might end up being my only console at university, which should breathe some life into it. The issue is that for short journeys (the daily commute) I really don't think it can compete with a smart phone. It can of course take some of the market, but anyone who has an iPhone/Android/WP7 (Blackberry?) will not take a PSP or DS because they don't need them.
Personally, I see the PSP as more of a console for when you are away for more extended periods of time, rather than something for everyday use. So to further that, a second analogue stick, trophies and better PSN support would be good.
If, however, Sony wants to go after the iPod touch market, then they need to change things more. The PSP go's form factor is much better, and with a lower price, things could be much better. I have said before, that I think Sony need to take advantage of cross-platform stuff more, so allow better connectivity between PS3 and PSP so you can play some of the same games on both. I also think a touch screen would be great for this, as it does help SOME games, even if in many cases physical controls are a must
As for games, allowing it to play Android games might be a start and using other Android apps, even if it is not a phone, so you could use the Android google map app through wi-fi. That would give it a large library of content, and with Sony's own content as well, it will have an unmatched level of games
I am not convinced that a PSP phone is the answer, as I feel for it to be a good phone, its PSPness might be comprimised, as the form factor for a phone is not right for gaming. My other major area of concern would be battery life. The PSPs is fairly rubbish as it is, and smart phones aren't that great and if you start to add in heavy gaming, then they basically disapear
So I'm not sure what Sony should do, but I think some integration with Android might be a good idea, and better PSN support would also be great. A touchscreen should probably be there, and probably a second analogue stick (but then you really need L2/R2 and I am not sure how you can make those and make it slim)