Engine stumbling

Having a weird issues with my vehicle that all seem to be connected.
1) At idle, the engine will on occasion slightly stumble for a second and then recover.
2) If I suddenly accelerate, my engine has that same feeling of stumbling/hesitating and will not accelerate very quickly. However, if I just casually press the gas down, I have no problems.
3) At highway speeds, if I casually press the gas (i.E. Give it just a little gas to maintain speed going up a hill) I again get that stumble/hesitation. If I really put some foot on the gas and raise the RPM's by 1,500, I have no stumbling/hesitation.

Through all of this, there have been no check engine lights. I took it to a mechanic to have them check the transmission, said that it has no problems and the only error codes in the computer are for a tilt sensor in the steering column. This all has me scratching my head, does anyone have any suggestions?