While flying straight and level, you were to partically lower the trailing edge flaps how would alter you aircarfts movements to remain at the same alititude etc?

I remember reading somewhere that a common practice with the 727 was for some captains to slightly extend the flaps or slats because they believed they got better true airspeed or economy or something. However, that just as many 727 pilots thought it was a crock.

It would certainly depend on the aircraft, some can only extend the flaps at increments of 10 degrees of so. Example would be with a Cherokee with a Johnson bar.

On the other hand with a newer C150 the flap switch is just a momentary contact switch and if you're not careful it's easy to leave the flaps partially extended. However the fowler flaps of the C150 just extend the cord slightly before they drop into the airflow so the effect isn't very noticeale. When bringing the flap up you have to listen to the different tone before the limit switch turns off the motor.

Flap settings and configurations vary depending the type of aircraft in question.  I am therefore going to furnish a very generic answer. 

In flight, the primary purpose of flaps is to add drag to the plane to slow it down. If you are flying straight/level and you lower the flaps, the plane is going to slow down. It won't change pitch, yaw, or roll so much as it will effect the airspeed. In order to hold altitude with flaps down, you have to apply more power. Other adjustments may accompany depending on the complexity of the plane. A throttle adjustment will help you maintain more control over altitude when the flaps are lowered.

Increase throttle and readjust altitude.