backlash on 85hp chrysler

[chrysler 01]

Hi ! I am new to boating and help somebody can help me out. I have a 1981 chrysler outboard model #858H1D that destroyed the pinion gear.I bought part# Fa498266 off a seller on ebay. With some help I was able to get the gearcase out and the pinion gear replaced. There seems to be too much play in the drive shaft or the propshaft . I would like to know how you measure backlash and how much is too much. The rest of the gears look good, bearing are good and show little wear.
I didn't see any water in the gear case when I drained it. My son would put into gear slowly,I was told you should snap it into gear and not baby it. is this true?