I have a 2000 Honda Accord. It's an older vehicle. I've had a few problems. I've had to replace 4 of the 6 coils, and I've replaced all tires.
Ever since I've had the car the engine over revs before changing gears. Sometimes there is a pause and then a bit of a jerk as I'm speeding up. Most of the time I can hear the whir of the engine as it over revs.
What would you assume is the problem? How much would the cost estimate be? Should I continue to drive it?

 

Verify the trans fluid is full.
If the fluid has not been changed think about having it changed.
Beg/borrow/steal an OBDII code reader/scanner.
Check for any codes, not all codes will set off the CEL.
Engine running condition will affect shift quality, even if the engine 'feels' fine an out of spec sensor will cause an incorrect load calculation which can lead to incorrect shifting.

Record and post all codes, not the description, here for further diagnostics.