In some cases directors will ask the stage manager to keep track of the lines missed of skipped by the actors. This places an additional burden on stage managers, especially those who are working on smaller contracts where they may be the only stage manager on a show and are trying to keep track of blocking, stay on line, and pay attention to the rehearsal action taking place in front of them.
If there are assistant directors I like to move the responsibility to them so that I may stay concentrated on the tasks unfolding in front of me.
If you must take line notes then try to make it as simple as possible. I like to keep a paper copy of the rehearsal report next to me that I can write on. As actors miss or invert lines I circle the lines or words on my script that they have missed and on the paper write the characters names and the page number (using my characters short hand from my blocking.) Then at the end of rehearsal I can call the actor over and go through the lines they missed and the pages that the lines are on.
Some directors want the line's missed emailed to the actors. I hope you don't have to do that but if you do come to an equitable arrangement with the director or you could be spending hours nightly typing up the line notes for the actors.
If on actor misses lines excessively you might consider asking for someone to work with them on their lines. I've done some shows where television stars have requested a reader to work on lines with them. Generally, the larger the name the more they can request and expect support. Considering all of the responsibilities the stage manager has it is more valuable for you to find someone who you can assign this task including your assistants if you have them.
It is also useful to remind the actors that learning their lines is an essential function of their job and working on their lines outside of rehearsal is a part of that job.