If your text is made up of thin lines and moving, you might be experiencing judder. That's where the horizontal and vertical edges are in slightly different positions relative to the pixel grid, so they antialias at different amounts, making the edges change color (or brightness) on each frame. If that is what is happening, you have two options. Make sure that the layer moves a whole number of pixels per frame using an expression. Judder is particularly noticeable in credit rolls when there is a lot of contrast between the text and the background, and the layer is moving at the wrong speed. There are also critical speeds where the frame rate and the movement create stroboscopic effects, causing the text layer to look like it is not moving smoothly or even changing directions. The problem is most noticeable at 24 fps and least noticeable at 60 fps.
You can hide antialiasing judder by adding motion blur. You can also reduce the effect by fattening up the characters and reducing the contrast between foreground and background.
The human eye's persistence of vision is equal to about 20 frames per second, so that's pretty close to the motion blur you get at about 1/50 of a second. The problem is that the brain can capture random images that last for about 1/200 of a second. When you combine those random images with motion blur you perceive when you are not following something on the screen and the stroboscopic studdering of the position and/or aliasing of the edges horizontal or vertical lines, you can not make moving thin lines in video or projected film always look perfectly smooth to all viewers, all the time. The best you can do is make sure they move at a whole number of pixels per frame or that they are thick enough that you don't notice the changing edge color.
I don't know if any of that helps. If we saw a screenshot or a screen recording of the problem, we would be better equipped to help you solve your problem.
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