I don't have answers, but it might help the regulars to help you if you could clarify whether your problem is in the screw (feeding manually) or in the gears (power feeding) - it is not clear whether you mean "It feels like the gears do not mesh smoothly" metaphorically, or literally...
Presumably you do have power cross feed with a taper attachment? In which case the first (or last from the transmissions perspective) gear is the one on the cross feed screw which meshes with the one that sticks up from the apron to transfer the drive. If someone has had the saddle off (4 big screws that are usually bound up solid and take a lot of effort to slacken) it is possible they didn't get the screw gear and the apron gear meshed properly when re-assembling (I've done it, but quickly worked it out), I would expect this just to lock the cross feed up solid, but if the saddle was not screwed down properly (look for a gap between it and the apron) then these gears may be touching but not meshed? Chock up your apron before investigating the screws, if you undo them it will otherwise only be supported by the leadscrew and you may bend it.
If it's not that and it is definitely gear related you might need to look at stripping the apron - it might be worth it to de-gunk the insides anyway, mine was full chips and old oil turned to grease.
If it's not the gears but the screw, maybe withdraw the screw and nut (again I'm sure this is a different operation with a taper attachment than I am used to) and check them, there are often replacement nuts for sale on ebay so if it is just a nut problem it may be quite easy to sort out. You mention a slot in the screw - I have no idea where this is or if it is likely to be a problem, but it is worth inspecting the threads - if they are very worn you might feel a stronger case for replacing it.
I presume the cross feed gib is adjusted properly and you are not simply experiencing it binding and causing the slide to jump when it frees itself? Depening on the age there may be a number of screws down the tailstock side of the slide that adjust it (parallel gib), or one locking screw on the side, and a big cheesehead screw accessible from the end which can pull or push a tapered gib to adjust it.
Finally of course, I guess you have taken the chipguard off (if possible with a taper attachment or does it replace the guard?) to make sure there isn't a big mass of curly chips wedged under it causing the problem?
Good luck troubleshooting!