I have 113 edit suggestions (81 approved and 32 edit rejected). However, when I check my badge progress in the review page, it says I have edited 80 posts. Why is this number not equal to the amount of edit suggestions approved (i.e. 81)?
Many statistics on the StackExchange family of sites are cached to reduce server contention. I'd wager badge progress pages aren't updated off most-recent data -- if only because I've sometimes been awarded badges hours after the corresponding event.
If it hasn't updated by the next day (check now, actually, the date has rolled over since you asked) then it might be more cause for concern.
In general, the sites converge towards correct over time -- you'll get the badges you earn eventually, even if it doesn't happen the second you submit the final required edit suggestion.