Ive noticed a few problems using a psp,
It's useless in any amount of natural light when watching movies and unuseable for games in sunlight. It has poor format support for both video and audio having no support for ogg or lossless formats unless you count wave, though admittedly it does support the best video codec (though no others). Videos however can't be played at full resolution, for some reason video playback is limited to 76,800 pixels while the screen is 130,576 pixels, it doesn't take a genius to work out that videos playing at half the res of the screen don't turn out fantastic.
Another annoyance is the limited frame rate support of 15fps and 29.97fps, meaning movies and tv episodes (in fact almost every video you put on the psp) need extra processing, increasing the already long time of encoding h.264 videos, and whats worse is that the psp video converters have almost no motion estimation resulting in blurry videos when the frame rate has been increased. You can't sort music properly on the psp either, when you put a folder inside another the psp doesn't recognize it, so don't plan on ordering music by artist and album because it simply doesn't work.
The web browser is slow and hard to navigate, unfortunately you have to use the cursed T9 method of typing, while this may work great on phones it doesn't work on a device where there is no physical keypad and it ends up being very very slow.....
And of course theres the battery, use wifi and its not going to last long at all, and the cost of a 3600mah one is £30, when you can buy 2xAA 2500mah rechargeable batteries for £2 thats outrageous and more proof that sony couldn't care less about the customer.