The Deputy tag on SO says:
Achieved a flag weight of 500 by reviewing and flagging appropriately
Does that mean I can get flag weight by reviewing?
If so, how?
If not, is this a mistake in the badge's description?
I think "reviewing and flagging appropriately" just means that reviewing is expected to precede flagging; it doesn't mean reviewing can by itself garner you flag weight.
No school will ever know whether you actually studied; they'll just see that you got good grades—but it's assumed that studying is a necessary antecedent to getting good grades. It's similarly assumed that reviewing is a necessary antecedent to making appropriate flags.
You could theoretically flag random posts, get extremely lucky and score glorious flag weight, but more likely than not you'll have to review first.