If you set up a Syslog server and want to keep all logs in a central location, make sure to create subfolders per node in the main folder as the first node to start logging will create a lock on the log files preventing any of the other nodes from logging. Additionally, when the node holding the locks is rebooted the locks will migrate to another node that starts logging and now you have to separate nodes logging to the same log. Both scenarios will prevent support from troubleshooting the issue at hand in the environment fully.
You can store coredumps on the SD boot media, but refrain from configuring the scratch partition here as the logs are write intensive and can cause the SD card to fail faster resulting in re-installation of ESXi
Minimum size of the SD card should be 16G
For servers that support SATADOM you can configure your scratch partition here, but refrain from using for coredumps as the partition cannot be resized automatically as needed to store the core file.