Keep A Calendar
I recommend that all parents sharing custody keep a custody calendar. A day planner or other notebook type calendar works best, giving you plenty of room to write details down. Make it a point to fill in the calendar each day noting important information such as when kids were dropped off, picked up, who drove to after school activities, phone calls, etc. You should also note communication with the other parent. Finally, keep receipts and other evidence to support your time sharing calendar entries.
Send A Confirming Email
As a lawyer, I do this all the time and its a pretty good habit to get into. Every time you and the other parent make an agreement regarding anything, send an email. An email provides a date and time, along with a written record of what was communicated. You could say something like "Dear Other Parent, this email is to confirm the agreement we just reached. You have agreed to take the kids to soccer this week and to return them to my home at 6:00 pm. If this is not what you agreed to, please let me know." This provides a record of both the agreement and the other parent's opportunity to "confirm" the agreement. If you get no response, the Court will see that your version of events was likely what really happened.