Transmission slipping?

I have a 1998 Honda Passport and the transmission is jumping when shifting in and out of 3rd gear.

However this does not happen every time?

Sometimes it will shift fine, and sometimes jumpy.

What seems to trigger the difference is when the Passport is started. If the transmission is shifting fine, then it usually will shift fine until the engine has been shut off. That is also true for the jumpy shifting (only 3rd gear). It will continue until you shut off the engine. (And until you are able to start it in the first condition with no jumping.)

When it is jumping it will make a sudden "Hard Shifting" (not a grind) noise as well as when it down shifts upon slowing to stop.

I do have problems with hard starts as well, and do not know if that might be related. I installed a new fuel filter and had a leak in the exhaust manifold repaired that was causing the O2 sensor to set off the engine light. I thought that might also fix the hard starts. But no luck. It does seem to start easier when I hold the ignition, for a few seconds, in the position just before it turns over. That seems to work more times then not. (Maybe a fuel pump going bad?)

Any help on the transmission would be greatly appreciated!

THANKS