Trouble with shaking speedometer; and trans

I'm having trouble with the speedometer on my 1991 explorer and it has a little over 200,000 miles. I put a new cable in for the speedometer and now it shakes back and forth, but it seems to only do this between 35-45 mph. And when it gets warmer outside it seems to shake a lot more. I replaced the speedometer gear and the actual speedometer itself. I also greased the cable. I don't know what else to do.

Also on a different problem, the car seems to run rough, but it just started doing that right after I had the transmission rebuilt. I had the fuel injectors cleaned and had an oil change and replaced the air filter. Please help me out.