Is the shaft nut stripped out? or is the blade just worn out?
No, the nut feels tight, it's just that the blade still wobbles even when it's tightened down as much as it'll go.
The blade might just have a big wow in it. Mowing at Rosie's is sortof like mowing a rock quarry :~D It's good she didn't get a real expensive mower, just she's gonna beat the crap out of it.