When something is malfunctioning, it's not very surprising when it malfunctions evenly and error reporting gets weird.
You should monitor server behaviour and throttle traffic back when it's close to its limits. I usually see things on monitored servers (check memory allocation over time - how much cache, how much process, how much kernel, iowait time, swap for sharp increases) in time to issue corrective measures.
Tuning maximum processes/threads on Apache seems one simple way to prevent that. Memcache and Varnish are also your friends with that - anything that prevents the workload from reaching Apache is.
