I went through something like that when I bought my current boat. As suggested you need to make sure that the lever at the tranmission is fully engaging in the gear and that neutral on the lever is at the detent for nuetral on the tranmission. For what it is worth. here is what I did, I disconnected the shft linkage from lever on the transmission. I taped a piece of cardboard to the top of the transmission so that the cardboard was was next to the lever. Using my hands to move the lever I carefully put the transmission into forward, reverse and neutral and very carely maked the position of the lever in each posistion. I then adjusted the linkage and lever stops so that the transmission was sinc'd with the lever.
The other thing is that the specific transmission fluid makes a huge difference. Read the manual and drain the transmission and put in the correct fluid. In my case, I followed the recommendation of an engine shop and had originally filled the transmission with a multiweight oil. I immediately noticed that the transmission did not seem to engage as well as I would have liked. I immediately went back to the recommendation in the manual and when I changed to the recommended single-weight oil, the transmission worked perfectly and has continued to do so.
I think that some small amount of rotation in neutral is not all that unusual.
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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay and part-time purveyor of marine supplies