My 66 does the same thing from 1st to 2nd. It is worn out. When it gets stuck I have to go under the hood and manually move the parts back in place. Once I figured out what is going on I just shifted carefully making sure I pull the shift lever towards me a little when going out of first then push a little back when going into 2nd. That is on my list to fix during the restore. My wife won't drive it until it is fixed.
As for it coming out of 3rd, it is possible the worn linkage is pulling it out of gear when you hit the gas and the motor and transmission rock a little pulling on the linkage. Not as likely as it being a transmission issue, but worth looking into.