Lets fix spot and hide. These need to be rolled by the hider, not the spotter. Having the spotter roll them provides metagame knowledge that there's something out there to spot. Having Spot be a simple DC which a hider must beat changes little in terms of the math of the game or the chances of success for a hider, but eliminates some of the metagame information derived from rolling to Spot. Sure, the player can see that the DM is rolling dice, but that could mean a lot of things. Its not quite as bad.
Or in the immortal words of Belkar, "I think I just failed a spot check."
Or in the immortal words of Belkar, "I think I just failed a spot check."