Reliable network event overflow

Does this just happen randomly, or are you actually trying to do something in FivePD? E.g. pull over a vehicle or accept a callout? Potentially one of the callouts is causing this, so you could maybe try disabling the callouts one by one using the Developer Menu?

He was driving around with the netEventLog open, to see what script was causing it. There were about 3 other people on the server. About 25 mins of driving the log started to send those messages like crazy before it kicked him for this error. 

I'm not one of the developers but I would think they're going to need a little bit more context in order to figure out what's causing it. I think it'll help a lot if you manage to get steps to reproduce the error. Also, I would suggest clearing out some of the callouts and see if the error persists. The reason I say this is, if this was an issue with core FivePD, I think it would've been a commonly reported error, which I don't think it is. It could be caused by one of the callouts.

Our server is also occasionally having this issue

You are not using oneSync, right?

Correct