Hey Aries,
Some questions for you:
1.) How did you configure your 6 ESXi 5.1 servers to send logs to Log Insight?
2.) How do you know that not all logs are being collected?
3.) What do you mean you are unable to view these logs interactively? Do you mean from the Interactive Analytics page? How are you trying to view them interactively (the more specific the better)?
4.) When you say you are unable to view certain chart widgets do you mean they are not returning results?
When configuring ESXi hosts to send logs to Log Insight, you need to be sure to configure the remote destination as well as the firewall (configure-esxi will handle both of these for you). In addition, if you are using TCP or SSL then you need to be aware that any connectivity issue between the ESXi host and a remote syslog destination will result in ESXi not sending remote logs without its syslog process being restarted (configure-esxi with the -r flag will handle this for you). Also note that some chart widgets may not display any results until a specific event occurs. One important thing to note is that only new logs since the remote syslog destination has been configured will be sent to Log Insight (i.e. not old logs). I hope this helps!