How do you reinstall lower unit on a 1974 9.8 mercury outboard motor so it will shift properly?

I am guessing that your shift is out of alignment on this little Merc. To correct this, the gearcase will have to be removed again. Once it is off, check to see if the gearcase is in neutral. This can be determined by turning the driveshaft in a clockwise direction while watching for prop movement. There will be no prop engagement in neutral gear. If there is prop movement, using slight pressure, turn the shiftshaft to the left, or to the right, to engage the neutral detent. Check to make sure the shift handle is also in the neutral position. Grease the shaft splines, and carefully reinstall. Take note that the watertube slides into the pump housing, and that the gearcase does not jump back into gear. The driveshaft splines can be aligned by rocking the flywheel back and forth.

Provided that the shift coupler is in serviceable condition, the engine should now shift properly.