That's not uncommon, this may or may not work, Try deleting them on the ipod and in itunes, then go to your purchased folder and re-download it, it won't charge you twice, in-spite of what the screen will tell you. I've done this a few times, the first time was with an apple tech guiding me through it.
Once that's done, then re-sync your ipod touch so itunes copies the fresh app onto your ipod again. Hopefully that helps.
If that fails you can reset the ipod, which may fix this too. And as a last resort there is always restoring the ipod and or contacting apple tech support too.
Apple told me that for some reason occasionally some apps won't work on our ipods for unknown reason, a glitch such as "Backgrounds"app on my 2nd gen ipod touch, so I just accepted it, and since all else is working very well I have just chosen to overlook it and move on.
