Transmission in 1996 mazda 626 slow to shift high rpm

You basically need the trans rebuilt. The only way the speed sensor could affect any of the shifting problems is if it broke off into the trans. somehow. You could try checking the trans fluid first, or having it changed.

Check fluid level, check vacume line to shift modulater on trans if there is an air leak it wont shift right if theres fluid in the line the modualator is bad .Change fluid and filter ad lucus trans treatment.

2nd gear pressure silinoid
check your fluid
check for vaccum leaks

Best thing to do is take it to a DEALER...not a transmission shop and have the fluid and filter changed. It will cost you about 200 bucks and they wont be so quick to tell you that a complete overhaul is needed.

Put about a cup of LUCAS transmission treatment in it after this is done. Great stuff to help the bands and smooth out shifting.

If this doesn't work you will likely need an overhaul if you are going to keep the car.
All this assuming your fluid level is not too high or too low, both of which can cause slippage.

shift cable or linkage is broke or poped off

Make sure you have the trany in "D" (drive) and not in a lower gear like 1,2 or 3. Some models must be in "econo" (not "power") setting for the trany to shift at a lower rpm. It will also get in overdrive sooner.

It seems as though the Transmission clutches are slipping if it's an automatic or the clutch is worn if it's a standard. If it's an automatic transmission check the Transmission oil it should be clean and no burnt smell. You will easily recognize burnt oil by it's nasty smell.

sounds like a shift solenoid in the trans.

Sounds Like You Broke an Axle, And Possibley Broke Something At The Transmission. Good Luck

Have you checked your transmission fluid? Be sure to read the owner's manual for the correct way to check this fluid.