Re: mercury 150 shift shaft
It will have some movement but 1" is a little much!
The shift shaft bushing has a rubber washer that sits on top of it, that is normal. Under the shift shaft is a C or E clip that keeps the shift shaft from coming out. That clip could be missing or came off.
Remove the lower unit from the engine. Get a shift shaft bushing tool, they are available aftermarket. Take the bushing out and install a new bushing. While removing the bushing hold down on the shift shaft!!!! DO not let it come out with the bushing.
Look at the shaft with the bushing out and see if the clip is there. If not replace the clip. Drain the gear oil and see if you can find the old one with a magnetic tool. You don't want it swimming in there.
If the shaft comes out you may have to disassemble the gearcase.