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Organization is good. Keep a calendar of all deadlines. Email out upcoming deadlines before every prod meeting, and keep in touch with designers regarding progress and likelihood of missing deadlines. If designers are behind, help them create action plans for getting the job done, or point them toward mentors/obi-wans/Rinaldi/assistance. Request and update a spreadsheet that has at minimum the following information for each scene: each actor in it and who they are playing, props needed, set, time/day, and any special effects (projection, blood). This helps figure out where quickchanges, set changes, or other technical elements may become problematic. An idea is to do this as a Google Spreadsheet that only the producer can edit, shared with the cast and crew by a link from Callboard.
Things You Should Make Sure Happen
Auditions
Read Through
This is the first rehearsal, sometimes preceded or succeeded by a cast/crew bonding event (such as Theater Games or a meal). This is generally scheduled by the SM, and if possible should be announced in the audition packet, and again when the cast list is announced.
Papertech
Papertech is when cue names, numbers, and timings are established by progressing from cue to cue through the text around a table. Minimum attendees are SM, Director, Lighting Designer, and Sound Designer. Costumes Designer, Set Designer, Props Designer, TD, Producer, and others should also be there depending on circumstances. Papertech is generally scheduled for the Saturday before the show opens, but this can be shifted slightly if necessary. The producer should make sure papertech scheduling is accounted for. Papertech is generally run by the SM. Run plans by the TD to make sure you are working in complementary strides with put-in.
Q2Q
Q2Q is the domain of the SM. It is either the evening at the end of put-in (Sunday before the show opens) or the next night (Monday). The more cues are written before Q2Q, the happier everyone will be. There is frequently (depending on the designers and other people involved) no point in having a Q2Q if less than a critical percent of the cues have been written. Actual actors are necessary to get heights and skin tones accounted for.