So, a quick run-down of ten of Vita's problems in my opinion, in no particular order:
1) Hasn't shifted the stigma in the West of having failed with the PSP, and the Vita being a PSP2.
2) Advertising, broadly speaking, has been poor. Having demo units in every large video game specialist? Excellent idea, however they're all gone and Sony hasn't done anything since, really.
3) Having too many games lined up for day 1. The Vita is conclusive proof that it's possible to have a launch lineup that's too good. The traditional barren six-to-nine months every console launch has (which we're still in) is emphasised further. Had half of the games that was released in day one been convinced to be released in the following six months, the "vita haz no gaems" stigma wouldn't have taken root as hard.
4) Sony of America is doing everything in its power to not sell the Vita outside of outright sabotage. It's probably the worst performance in selling a console by an American arm since the Sega Saturn.
5) No UMD support, while understandable, has harmed its chances in Japan.
6) Japanese developers being really slow to transition from the PSP to the Vita, and may instead transition towards the 3DS and reuse their PSP assets.
7) Letting the 3DS position itself as the PSP2 in Japan, especially with regard to Monster Hunter sequels.
8) Still no PS1 support.
9) Playstation Mobile is still in gestation, and more than likely will be dead on arrival.
10) Sony of America's focus on straight ports and letting previously Vita exclusive games get ported onto the PS3 is an extremely bad idea (see also 4).