The stage manager tracks things like start time, intermission length, technical issues, etc. and they send a nightly performance report. They'll also note which understudies were on, who conducted the performance, which of the SMs called the show, if something broke, if something was late, if they had to modify part of the set to fit the venue, etc etc etc. And they'll offer a little assessment of the performance ("small but friendly house tonight, lots of laughs during <song>, etc) and sometimes they even note the weather.
The resident director's role is primarily giving notes to the actors to keep the show consistent to the original director's vision and improve their performances. Or, on a technical level, things like "can we take a look at her wig, it's not sitting right."